Explicit Fusion Data for Small Association Schemes

Allen Herman
(Department of Mathematics and Statistics, University of Regina, Canada)
and
Sourav Sikdar
(Department of Computer Science & Engineering, Faculty of Engineering & Technology, Jadavpur University, India).

First update: September 20, 2011; Latest update: May 27, 2013.

Acknowledgements

This reports the results of the MITACS Globalink project "Classification of Small Association Schemes", which the authors collaborated on during the months of June to August, 2011.
The project was supported by the MITACS Globalink program. Computing facilities were provided by the Labratory of Computational Discovery at the University of Regina, and our programming was done using the Computer Algebra Program GAP: Groups, Algorithms, and Programming.

Order 6 to 8 .
Order 9 to 11 .
Order 12 .
Order 13 to 15 .
Order 16
Order 17 and 18 .
Order 19 and 20 .
Order 21 to 23 .
Order 24 (Possibly incomplete: see warnings)
Order 25 . Order 26 .
Order 27
Order 28 (Possibly incomplete: see warnings)
Order 29 . Order 30 .

The Project

We give explicit fusion data for small association schemes of orders 6 to 30. All the maximal fusions we record are confirmed. For schemes of order 24 and 28, we are unable to completely verify that all fusions have been detected. The schemes are listed according to the classification of small association schemes of order up to 30 that has been completed by A. Hanaki and I. Miyamoto on their kissme website . To be more precise, the input for our computer program is their ordered list of schemes of a given order, appended by the ordered list of thin schemes of order n generated using GAP's group library. For each scheme S_i in the list of schemes of order n, the program outputs the list of schemes S_j of the same order that are maximal fusions of S_i. For each maximal fusion, we provide explicit data in the form of an ordered partition p and a permutation τ of {1,...,n} for which the basic matrix B_j of S_j is obtained from that of that of S_i by fusing according to the ordered partition p, forming the basic matrix of the fused scheme, and then conjugating it with the n×n permutation matrix corresponding to τ, which is chosen to be the identity permutation ( ) whenever possible.

The Computer Program

Our program is written entirely in GAP. It detects if a scheme S_j is a fusion of scheme S_i using one of two methods. The first method is based on partitions, the second is purely algebraic. The basic code for the programs we used is here.

In the partition method, if the scheme S_i has d classes, and the scheme S_j has k classes with d > k, we search PartitionSet([1..d],k) for a partition Q for which FusionScheme(S_i,Q) is combinatorially isomorphic to S_j. It starts by extracting the partitions of [1..d] of size k for which the first row of the basic matrix of FusionScheme(S_i,Q) matches that of S_j. The number of partitions to be searched can be very large, but this method is still fairly effective as long as PartitionSet([1..d],k) has size less than one million. When the number of partitions was larger than a million, the algebraic method was more productive despite being more prone to crashes and freezes than the partition method. We then searched this subset of the partitions until we found a permutation τ that would map the basic matrix of FusionScheme(S_i,Q) to that of S_i. The data for the explicit fusion of S_i to S_j is recorded in this case as i-->j: [Q,τ] below.

In the algebraic method, we start by calculating the combinatorial automorphism groups G_i and G_j of the two schemes. A necessary condition for fusion is that the size of G_i must be combinatorially isomorphic to a subgroup of G_j. Although the performance of GAP's programs for testing this can be erratic sometimes, they are effective when the groups involved have smaller Sylow subgroups. After applying a permutation τ so that G_i was a subgroup of G_j, we then formed the rational vector space spanned by the adjacency matrices of S_i, and expressed the basic matrix of S_j in terms of its basis of adjacency matrices. The coefficients of this expression is then used to generate the partition Q needed for the fusion. In this case, the data for the explicit fusion is recorded as i-->j: [τ, Q].

Order 6: Groups: Nos. 7,8.
Fusions6 := [ [ [ 1, [ ] ], [ 2, [ 1 ] ], [ 3, [ 1 ] ], [ 4, [ 3 ] ], [ 5, [ 2, 3 ] ], [ 6, [ 2 ] ], [ 7, [ 4, 5 ] ], [ 8, [ 4, 5, 6 ] ] ] ];

Explicit Fusions:
4-->3: [ [ 1, 2 ], [ 3 ] ],() )
5-->3: ([ [ 2 ], [ 1, 3 ] ],(1,4,6,2,3,5) )
5-->2: ([ [ 1 ], [ 2, 3 ] ],(1,5,2,6,4,3) )
6-->2: ([ [ 1 ], [ 2, 3 ] ],() )
7-->5: ([ [ 3 ], [ 1, 2 ], [ 4, 5 ] ],(2,4) )
7-->4: ([ [ 1 ], [ 2 ], [ 3, 4, 5 ] ],() )
8-->6: ([ [ 3 ], [ 2, 5 ], [ 1, 4 ] ],(2,3,5,4) )
8-->5: ([ [ 3 ], [ 1, 2 ], [ 4, 5 ] ],(2,3,4) )
8-->4: ([ [ 1 ], [ 2 ], [ 3, 4, 5 ] ],() )

Order 7: Group: No. 4.
Fusions7 := [ [ 1, [ ] ], [ 2, [ 1 ] ], [ 3, [ 1 ] ], [ 4, [ 2, 3 ] ] ];

Explicit Fusions:
4-->3: ([ [ 2, 5 ], [ 3, 4 ], [ 1, 6 ] ],(2,3,5,6,4,7) )
4-->2: ([ [ 3, 5, 6 ], [ 1, 2, 4 ] ],(2,7)(3,6) )

Order 8: Groups: Nos. 17 to 21.
Fusions8 := [ [ 1, [ ] ], [ 2, [ 1 ] ], [ 3, [ 1 ] ], [ 4, [ 2, 3 ] ], [ 5, [ 2, 3 ] ], [ 6, [ 2 ] ], [ 7, [ 4 ] ], [ 8, [ 4 ] ], [ 9, [ 4 ] ], [ 10, [ 4 ] ], [ 11, [ 4 ] ], [ 12, [ 4 ] ], [ 13, [ 5, 7, 9 ] ], [ 14, [ 7, 11 ] ], [ 15, [ 8, 9 ] ], [ 16, [ 8, 11 ] ], [ 17, [ 10, 12, 16 ] ], [ 18, [ 13, 14, 15 ] ], [ 19, [ 10, 13, 15 ] ], [ 20, [ 6, 12, 15 ] ], [ 21, [ 13 ] ] ];

Explicit Fusions:
4-->3: ([ [ 1, 2 ], [ 3 ] ],() )
4-->2: ([ [ 1 ], [ 2, 3 ] ],() )
5-->3: ([ [ 2 ], [ 1, 3 ] ],(1,5,8,3,6)(2,4,7) )
5-->2: ([ [ 1 ], [ 2, 3 ] ],(1,3,5,7)(2,4) )
6-->2: ([ [ 1 ], [ 2, 3 ] ],(1,3,5,7,8)(2,4) )
7-->4: ([ [ 1 ], [ 2, 3 ], [ 4 ] ],() )
8-->4: ([ [ 1 ], [ 2, 3 ], [ 4 ] ],() )
9-->4: ([ [ 1 ], [ 2 ], [ 3, 4 ] ],() )
10-->4: ([ [ 1 ], [ 2 ], [ 3, 4 ] ],(1,5)(2,6,3,7,4,8) )
11-->4: ([ [ 1 ], [ 2 ], [ 3, 4 ] ],() )
12-->4: ([ [ 1 ], [ 2 ], [ 3, 4 ] ],(1,5)(2,6,3,7,4,8) )
13-->9: ([ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ] ],() )
13-->7: ([ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ],() )
13-->5: ([ [ 2 ], [ 1, 4 ], [ 3, 5 ] ],(1,3,6)(2,4,7,8) )
14-->11: ([ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ] ],() )
14-->7: ([ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ],() )
15-->9: ([ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ] ],() )
15-->8: ([ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ],() )
16-->11: ([ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ] ],() )
16-->8: ([ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ],() )
17-->16: ([ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ], [ 6, 7 ] ],() )
17-->12: ([ [ 1 ], [ 2, 3 ], [ 4, 6 ], [ 5, 7 ] ],(3,4)(5,8,6) )
17-->10: ([ [ 1 ], [ 2, 3 ], [ 4, 7 ], [ 5, 6 ] ],(3,4)(5,6,7,8) )
18-->15: ([ [ 1 ], [ 4 ], [ 5 ], [ 2, 3 ], [ 6, 7 ] ],(3,5,4,6)(7,8) )
18-->14: ([ [ 2 ], [ 1 ], [ 3 ], [ 4, 6 ], [ 5, 7 ] ],(2,3)(5,7,8,6) )
18-->13: ([ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ], [ 6, 7 ] ],() )
19-->15: ([ [ 1 ], [ 7 ], [ 6 ], [ 4, 5 ], [ 2, 3 ] ],(3,5,7,4,6,8) )
19-->13: ([ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ], [ 6, 7 ] ],() )
19-->10: ([ [ 1 ], [ 6, 7 ], [ 2, 4 ], [ 3, 5 ] ],(3,5,6,7,4,8) )
20-->15: ([ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ], [ 6, 7 ] ],() )
20-->12: ([ [ 1 ], [ 2, 3 ], [ 4, 7 ], [ 5, 6 ] ],(6,8,7) )
20-->6: ([ [ 1 ], [ 2, 5, 7 ], [ 3, 4, 6 ] ],(4,6,8,7,5) )
21-->13: ([ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ], [ 6, 7 ] ],() )

Order 9: Groups: Nos. 11, 12.
Fusions9 := [ [ 1, [ ] ], [ 2, [ 1 ] ], [ 3, [ 1 ] ], [ 4, [ 2 ] ], [ 5, [ 2, 3 ] ], [ 6, [ 2 ] ], [ 7, [ 4, 6 ] ], [ 8, [ 5 ] ], [ 9, [ 2 ] ], [ 10, [ 4, 5, 6 ] ], [ 11, [ 7, 9 ] ], [ 12, [ 7, 8, 10 ] ] ];

Explicit Fusions:
4-->2: ( [ [ 1, 2 ], [ 3 ] ], (( )) )
5-->3: ( [ [ 1, 2 ], [ 3 ] ], (( )) )
5-->2: ( [ [ 1 ], [ 2, 3 ] ] )
6-->2: ( [ [ 1 ], [ 2, 3 ] ], (( )) )
7-->6: ( [ [ 1, 2 ], [ 3 ], [ 4 ] ], (( )) )
7-->4: ( [ [ 1 ], [ 2 ], [ 3, 4 ] ], (( )) )
8-->5: ( [ [ 1 ], [ 2 ], [ 3, 4 ] ] )
9-->2: ( [ [ 1 ], [ 2, 3, 4 ] ] )
10-->6: ( [ [ 1, 5 ], [ 2, 4 ], [ 3 ] ] )
10-->5: ( [ [ 1, 2 ], [ 3 ], [ 4, 5 ] ] )
10-->4: ( [ [ 1 ], [ 2 ], [ 3, 4, 5 ] ] )
11-->9: ([ [ 1, 2 ], [ 3, 8 ], [ 5, 6 ], [ 4, 7 ] ],(1,4)(2,7,5,3,8,9,6))
11-->7: ([ [ 1 ], [ 2 ], [ 3, 4, 5 ], [ 6, 7, 8 ] ],())
12-->10: ([ [ 1 ], [ 2 ], [ 3, 6 ], [ 5, 8 ], [ 4, 7 ] ],(1,7,6,2,5)(3,9,8,4))
12-->8: ([ [ 1, 2 ], [ 3, 6 ], [ 4, 8 ], [ 5, 7 ] ],(1,5,3,6,2,9,8,7,4 ))
12-->7: ([ [ 1 ], [ 2 ], [ 3, 4, 5 ], [ 6, 7, 8 ] ],())

Order 10: Groups: Nos. 12, 13.
Fusions10 := [ [ 1, [ ] ], [ 2, [ 1 ] ], [ 3, [ 1 ] ], [ 4, [ 1 ] ], [ 5, [ 2 ] ], [ 6, [ 2, 4 ] ], [ 7, [ 4 ] ], [ 8, [ 7 ] ], [ 9, [ 5, 6, 7 ] ], [ 10, [ 3, 6, 7 ] ], [ 11, [ 5 ] ], [ 12, [ 8, 9 ] ], [ 13, [ 8, 9, 11 ] ] ];

Explicit Fusions:
5-->2: ( [ [ 1 ], [ 2, 3 ] ], (( )) )
6-->4: ( [ [ 1, 3 ], [ 2 ] ] ),
6-->2: ( [ [ 1 ], [ 2, 3 ] ] )
7-->4: ( [ [ 1, 2 ], [ 3 ] ], (( )) )
8-->7: ( [ [ 1, 2 ], [ 3, 4 ], [ 5 ] ] )
9-->7: ( [ [ 1, 3, 5 ], [ 2 ], [ 4 ] ] ),
9-->6: ( [ [ 1 ], [ 2, 4 ], [ 3, 5 ] ] ),
9-->5: ( [ [ 1 ], [ 2, 3 ], [ 4, 5 ] ] )
10-->7: ( [ [ 1, 4, 5 ], [ 2 ], [ 3 ] ] ),
10-->6: ( [ [ 1 ], [ 2, 3 ], [ 4, 5 ] ] ),
10-->3: ( [ [ 1, 2 ], [ 3, 4, 5 ] ] )
11-->5: ( [ [ 1 ], [ 2, 3 ], [ 4, 5 ] ] )
12-->9: ([ [ 5 ], [ 1, 4 ], [ 6, 9 ], [ 2, 3 ], [ 7, 8 ] ],( 1, 4, 7,10, 2)( 5, 8, 9))
12-->8: ([ [ 1 ], [ 4 ], [ 3 ], [ 2 ], [ 5, 6, 7, 8, 9 ] ],( 1, 8, 2, 6, 3, 7)( 4,10)( 5, 9))
13-->11: ([ [ 5 ], [ 1, 6 ], [ 4, 9 ], [ 3, 8 ], [ 2, 7 ] ],( 1, 9, 2, 7, 8, 5, 3, 6,10, 4))
13-->9: ([ [ 5 ], [ 1, 4 ], [ 6, 9 ], [ 2, 3 ], [ 7, 8 ] ],( 1, 7,10, 5, 3, 4)( 2, 8, 6, 9))
13-->8: ([ [ 1 ], [ 4 ], [ 3 ], [ 2 ], [ 5, 6, 7, 8, 9 ] ],( 1, 8, 2, 6, 3, 7)( 4,10)( 5, 9))

Order 11: Group: No. 4.
Fusions11 := [ [ 1, [ ] ], [ 2, [ 1 ] ], [ 3, [ 1 ] ], [ 4, [ 2, 3 ] ] ];

Explicit Fusions:
4-->3: ([ [ 1, 10 ], [ 2, 9 ], [ 3, 8 ], [ 4, 7 ], [ 5, 6 ] ],( 1,11, 9, 5, 4, 6, 2,10, 7)( 3, 8))
4-->2: ([ [ 1, 3, 4, 5, 9 ], [ 2, 6, 7, 8, 10 ] ],( 1, 9, 4,11, 7,10, 5)( 2, 8)( 3, 6))

Order 12: Groups: Nos. 55 to 59.
Fusions12 := [ [ 1, [ ] ], [ 2, [ 1 ] ], [ 3, [ 1 ] ], [ 4, [ 1 ] ], [ 5, [ 1 ] ], [ 6, [ 3 ] ], [ 7, [ 2, 4 ] ], [ 8, [ 2, 5 ] ], [ 9, [ 2, 5 ] ], [ 10, [ 2 ] ], [ 11, [ 3, 5 ] ], [ 12, [ 3, 4 ] ], [ 13, [ 4 ] ], [ 14, [ 7 ] ], [ 15, [ 7 ] ], [ 16, [ 6, 11 ] ], [ 17, [ 8, 11 ] ], [ 18, [ 8 ] ], [ 19, [ 7, 8 ] ], [ 20, [ 7 ] ], [ 21, [ 7, 13 ] ], [ 22, [ 7 ] ], [ 23, [ 11 ] ], [ 24, [ 11 ] ], [ 25, [ 9, 14, 19 ] ], [ 26, [ 14, 21 ] ], [ 27, [ 15, 19 ] ], [ 28, [ 15, 21 ] ], [ 29, [ 16, 23 ] ], [ 30, [ 16, 24 ] ], [ 31, [ 6, 12, 13 ] ], [ 32, [ 12, 17, 19 ] ], [ 33, [ 9, 17, 23 ] ], [ 34, [ 17, 24 ] ], [ 35, [ 16, 17 ] ], [ 36, [ 16, 17, 18 ] ], [ 37, [ 32 ] ], [ 38, [ 18, 19 ] ], [ 39, [ 32 ] ], [ 40, [ 12, 20 ] ], [ 41, [ 18, 19, 21 ] ], [ 42, [ 29, 33, 35 ] ], [ 43, [ 30, 34, 35 ] ], [ 44, [ 29, 33, 36 ] ], [ 45, [ 30, 34, 36 ] ], [ 46, [ 25, 32, 33 ] ], [ 47, [ 25, 38 ] ], [ 48, [ 25, 26, 41 ] ], [ 49, [ 10, 20, 22, 26 ] ], [ 50, [ 27, 38 ] ], [ 51, [ 27, 32, 34 ] ], [ 52, [ 27, 28, 41 ] ], [ 53, [ 32, 36, 38 ] ], [ 54, [ 31, 32, 36, 41 ] ], [ 55, [ 22, 39, 45, 50, 51, 53 ] ], [ 56, [ 37, 45, 51, 52, 54 ] ], [ 57, [ 31, 40, 49 ] ], [ 58, [ 37, 42, 44, 46, 47, 53 ] ], [ 59, [ 39, 44, 46, 48, 54 ] ] ];

Explicit Fusions:
6-->3:[ [ [ 1, 2 ], [ 3 ] ], () ]
7-->4:[ [ [ 1, 2 ], [ 3 ] ], () ]
7-->2:[ [ [ 1 ], [ 2, 3 ] ], () ]
8-->5:[ [ [ 1, 2 ], [ 3 ] ], () ]
8-->2:[ [ [ 1 ], [ 2, 3 ] ], () ]
9-->5:[ [ [ 1, 3 ], [ 2 ] ], ( 2, 3, 4, 5, 6, 7) ]
9-->2:[ [ [ 1 ], [ 2, 3 ] ], ( 4, 8,10,11, 7, 5)( 6, 9) ]
10-->2:[ [ [ 1 ], [ 2, 3 ] ], ( 4, 8,12, 9, 6,11, 7, 5) ]
11-->5:[ [ [ 1, 2 ], [ 3 ] ], () ]
11-->3:[ [ [ 1 ], [ 2, 3 ] ], () ]
12-->4:[ [ [ 1, 3 ], [ 2 ] ], ( 2, 4, 6, 7, 8, 9, 3, 5) ]
12-->3:[ [ [ 1 ], [ 2, 3 ] ], ( 5, 7)( 6,10)( 9,11) ]
13-->4:[ [ [ 1 ], [ 2, 3 ] ], () ]
14-->7:[ [ [ 1 ], [ 2, 3 ], [ 4 ] ], () ]
15-->7:[ [ [ 1 ], [ 2, 3 ], [ 4 ] ], () ]
16-->11:[ [ [ 1, 2 ], [ 3 ], [ 4 ] ], () ]
16-->6:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], () ]
17-->11:[ [ [ 1, 3 ], [ 2 ], [ 4 ] ], ( 2, 3, 4)( 8, 9,10) ]
17-->8:[ [ [ 1 ], [ 2, 3 ], [ 4 ] ], ( 4, 5)(10,11) ]
18-->8:[ [ [ 1 ], [ 2, 3 ], [ 4 ] ], () ]
19-->8:[ [ [ 1 ], [ 2, 4 ], [ 3 ] ], ( 3, 5, 7)( 4, 6, 8) ]
19-->7:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], ( 7, 9)( 8,10) ]
20-->7:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], ( 6,11, 8,12, 9, 7) ]
21-->13:[ [ [ 1, 2 ], [ 3 ], [ 4 ] ], () ]
21-->7:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], () ]
22-->7:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], ( 6,11, 8,12, 9, 7) ]
23-->11:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], () ]
24-->11:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], () ]
25-->19:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ] ], () ]
25-->14:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], ( 7, 9)( 8,10) ]
25-->9:[ [ [ 1, 4 ], [ 2 ], [ 3, 5 ] ], ( 2, 3)( 4, 5, 6, 7, 8) ]
26-->21:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ] ], () ]
26-->14:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], () ]
27-->19:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ] ], () ]
27-->15:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], ( 7, 9)( 8,10) ]
28-->21:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ] ], () ]
28-->15:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], () ]
29-->23:[ [ [ 1, 2 ], [ 3 ], [ 4 ], [ 5 ] ], () ]
29-->16:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], () ]
30-->24:[ [ [ 1, 2 ], [ 3 ], [ 4 ], [ 5 ] ], () ]
30-->16:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], () ]
31-->13:[ [ [ 1, 5 ], [ 2, 4 ], [ 3 ] ], ( 2, 4, 6,10, 7,11, 8,12, 9, 3, 5)]
31-->12:[ [ [ 1, 2 ], [ 3 ], [ 4, 5 ] ],( 2, 3)( 4, 5, 6)( 7, 8, 9)(10,11,12) ]
31-->6:[ [ [ 1 ], [ 2 ], [ 3, 4, 5 ] ],( 2, 3)( 4,12)( 5, 6, 9, 8)( 7,11,10) ]
32-->19:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5 ] ], ( 6, 7)(10,11) ]
32-->17:[ [ [ 1 ], [ 2, 5 ], [ 3 ], [ 4 ] ], ( 3, 5, 7)( 4, 6, 8) ]
32-->12:[ [ [ 1, 2 ], [ 3 ], [ 4, 5 ] ], ( 2, 5, 3, 6, 4)( 8, 9,11,10) ]
33-->23:[ [ [ 1, 3 ], [ 2 ], [ 4 ], [ 5 ] ], ( 2, 3, 4) ]
33-->17:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], ( 8,10, 9) ]
33-->9:[ [ [ 1 ], [ 2, 4 ], [ 3, 5 ] ], ( 5, 7, 9, 6, 8) ]
34-->24:[ [ [ 1, 3 ], [ 2 ], [ 4 ], [ 5 ] ], ( 2, 3, 4) ]
34-->17:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], ( 8,10, 9) ]
35-->17:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ], [ 6 ] ],( 3, 5, 4, 6)( 7, 9,10, 8,12) ]
35-->16:[ [ [ 1, 2, 3 ], [ 4 ], [ 5 ], [ 6 ] ],( 2, 5, 3, 6, 4)( 8,11, 9,12,10) ]
36-->18:[ [ [ 1 ], [ 2, 4 ], [ 3, 5 ], [ 6 ] ], ( 4, 5)(10,11) ]
36-->17:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ], [ 6 ] ], () ]
36-->16:[ [ [ 1, 4, 5 ], [ 2 ], [ 3 ], [ 6 ] ], ( 2, 3, 4)( 8, 9,10) ]
37-->32:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5, 6 ] ], ( 3, 4)( 7, 8)( 9,10,12)]
38-->19:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5, 6 ] ], ( 5, 9, 7,11)( 6,10, 8,12)]
38-->18:[ [ [ 1 ], [ 2, 3, 4 ], [ 5 ], [ 6 ] ],( 3, 9, 5,11, 7)( 4,10, 6,12, 8) ]
39-->32:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5, 6 ] ], ( 3, 4)( 5, 6)( 9,10,12)]
40-->20:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5, 6 ] ], ( 6, 7)(10,11,12) ]
40-->12:[ [ [ 1, 2 ], [ 3 ], [ 4, 5, 6 ] ],( 2, 6, 4, 3, 5)( 7,11,10)( 8, 9) ]
41-->21:[ [ [ 1 ], [ 2 ], [ 3, 5 ], [ 4, 6 ] ], ( 7, 9)( 8,10) ]
41-->19:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5, 6 ] ], () ]
41-->18:[ [ [ 1 ], [ 2, 5, 6 ], [ 3 ], [ 4 ] ], ( 3, 5, 7)( 4, 6, 8) ]
42-->35:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6, 7 ] ], ( 8,10,12, 9,11)]
42-->33:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ], [ 6 ], [ 7 ] ],( 3, 5, 4, 6)( 7,12)( 8,11, 9,10) ]
42-->29:[ [ [ 1, 2, 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ] ], ( 2, 5, 3, 6, 4) ]
43-->35:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6, 7 ] ], ( 8,10,12, 9,11)]
43-->34:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ], [ 6 ], [ 7 ] ],( 3, 5, 4, 6)( 7,12)( 8,11, 9,10) ]
43-->30:[ [ [ 1, 2, 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ] ], ( 2, 5, 3, 6, 4) ]
44-->36:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6, 7 ] ], ( 8,10, 9) ]
44-->33:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ], [ 6 ], [ 7 ] ], () ]
44-->29:[ [ [ 1, 4, 5 ], [ 2 ], [ 3 ], [ 6 ], [ 7 ] ], ( 2, 3, 4) ]
45-->36:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6, 7 ] ], ( 8,10, 9) ]
45-->34:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ], [ 6 ], [ 7 ] ], () ]
45-->30:[ [ [ 1, 4, 5 ], [ 2 ], [ 3 ], [ 6 ], [ 7 ] ], ( 2, 3, 4) ]
46-->33:[ [ [ 1 ], [ 2, 6 ], [ 3, 7 ], [ 4 ], [ 5 ] ],( 3, 5, 7)( 4, 6, 8, 9,10) ]
46-->32:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ], [ 6, 7 ] ], () ]
46-->25:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ], [ 6, 7 ] ], ( 6, 7)(10,11) ]
47-->38:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ] ], () ]
47-->25:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ], [ 6, 7 ] ],( 3, 4)( 5,10, 8,12)( 6, 9, 7,11) ]
48-->41:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ] ], () ]
48-->26:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 6 ], [ 5, 7 ] ], ( 7, 9)( 8,10) ]
48-->25:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ], [ 6, 7 ] ], () ]
49-->26:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 7 ], [ 5, 6 ] ],( 2, 3, 4)( 5, 8, 7, 9,12, 6,10,11) ]
49-->22:[ [ [ 1, 2 ], [ 3 ], [ 4, 6 ], [ 5, 7 ] ],( 2, 4)( 5, 9,12, 7, 6,10,11, 8) ]
49-->20:[ [ [ 1, 2 ], [ 3 ], [ 4, 5 ], [ 6, 7 ] ], ( 2, 4, 3)(11,12) ]
49-->10:[ [ [ 1, 4, 5 ], [ 2, 6, 7 ], [ 3 ] ], ( 2, 4, 5, 6, 7, 8, 3)(11,12)]
50-->38:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ] ], () ]
50-->27:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ], [ 6, 7 ] ],( 3, 4)( 5, 9, 7,12)( 6,10, 8,11) ]
51-->34:[ [ [ 1 ], [ 2, 7 ], [ 3, 6 ], [ 4 ], [ 5 ] ],( 3, 6, 7, 9, 4, 5, 8,10,11,12) ]
51-->32:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ], [ 6, 7 ] ],( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12) ]
51-->27:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ], [ 6, 7 ] ],( 3, 4)( 5, 6, 8)( 9,10,12) ]
52-->41:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ] ], () ]
52-->28:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 6 ], [ 5, 7 ] ], ( 7, 9)( 8,10) ]
52-->27:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ], [ 6, 7 ] ], () ]
53-->38:[ [ [ 1 ], [ 2, 4 ], [ 3, 5 ], [ 6 ], [ 7 ], [ 8 ] ],( 3, 7,11, 4, 8,12, 6,10, 5, 9) ]
53-->36:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6, 7, 8 ] ], (10,11) ]
53-->32:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ], [ 6 ], [ 7, 8 ] ],( 3, 7, 5)( 4, 8, 6)( 9,11,12,10) ]
54-->41:[ [ [ 1 ], [ 2, 4 ], [ 3, 5 ], [ 6 ], [ 7 ], [ 8 ] ],( 3, 7, 4, 8, 6, 5)( 9,11)(10,12) ]
54-->36:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6, 7, 8 ] ],( 3, 4)( 5, 6)( 7, 9,11,12, 8,10) ]
54-->32:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ], [ 6 ], [ 7, 8 ] ],( 3, 7, 5)( 4, 8, 6)( 9,11,12,10) ]
54-->31:[ [ [ 1, 6 ], [ 2 ], [ 3 ], [ 4, 8 ], [ 5, 7 ] ], ( 2, 4, 8,11, 9, 5, 7,12, 6) ]
55-->53:[ ( 2, 3, 4)( 8, 9,11,10), [ [ 3 ], [ 1 ], [ 2 ], [ 4 ], [ 5 ], [ 6, 9 ], [ 7, 10 ], [ 8, 11 ] ] ]
55-->51:[ ( 2, 6, 7, 4)( 3, 5, 8, 9,10), [ [ 3 ], [ 9 ], [ 6 ], [ 1, 2 ], [ 4, 5 ], [ 7, 8 ], [ 10, 11 ] ] ]
55-->50:[ ( 2,11, 8, 7, 4)( 3, 9, 5,12, 6,10), [ [ 3 ], [ 9 ], [ 6 ], [ 8, 11 ], [ 7, 10 ], [ 2, 5 ], [ 1, 4 ] ] ]
55-->45:[ ( 2, 3, 4), [ [ 3 ], [ 1 ], [ 2 ], [ 4 ], [ 5 ], [ 6, 7, 8 ], [ 9, 10, 11 ] ] ]
55-->39:[ ( 2, 6, 8,12,11, 9,10, 3, 5, 7, 4), [ [ 3 ], [ 6, 9 ], [ 1, 2 ], [ 4, 5 ], [ 8, 10 ], [ 7, 11 ] ] ]
55-->22:[ ( 2, 7, 4)( 3,11, 6, 5,10)( 8,12), [ [ 3 ], [ 6, 9 ], [ 1, 5, 10, 11 ], [ 2, 4, 7, 8 ] ] ]
56-->54:[ ( 4, 5)( 9,11)(10,12), [ [ 1 ], [ 2 ], [ 4 ], [ 3 ], [ 5 ], [ 6, 7 ], [ 10, 11 ], [ 8, 9 ] ] ]
56-->52:[ ( 3, 8)( 4, 7)( 9,11,10,12), [ [ 1 ], [ 7 ], [ 6 ], [ 4, 5 ], [ 2, 3 ], [ 10, 11 ], [ 8, 9 ] ] ]
56-->51:[ ( 3, 6, 7, 4, 8)( 9,10,12,11), [ [ 1 ], [ 7 ], [ 6 ], [ 2, 4 ], [ 3, 5 ], [ 8, 10 ], [ 9, 11 ] ] ]
56-->45:[ ( 4, 5)( 7, 8,11)(10,12), [ [ 1 ], [ 2 ], [ 4 ], [ 3 ], [ 5 ], [ 6, 8, 10 ], [ 7, 9, 11 ] ] ]
56-->37:[ ( 3, 6, 8)( 4, 7)( 9,12,11,10), [ [ 1 ], [ 6, 7 ], [ 2, 4 ], [ 3, 5 ], [ 9, 10 ], [ 8, 11 ] ] ]
57-->49:[ ( 5, 7, 9)( 6, 8,10,11), [ [ 1 ], [ 2 ], [ 3 ], [ 8, 10 ], [ 4, 5 ], [ 6, 7 ], [ 9, 11 ] ] ]
57-->40:[ ( 5, 6,11,10,12, 7, 8, 9), [ [ 1 ], [ 2, 3 ], [ 4, 8 ], [ 6, 11 ], [ 7, 10 ], [ 5, 9 ] ] ]
57-->31:[ ( 2, 4, 6,11, 7,12, 8,10, 9, 3, 5), [ [ 4 ], [ 8 ], [ 1, 2, 3 ], [ 9, 10, 11 ], [ 5, 6, 7 ] ] ]
58-->53:[ ( 2, 3, 4)( 8, 9,11,10), [ [ 3 ], [ 1 ], [ 2 ], [ 4 ], [ 5 ], [ 6, 9 ], [ 7, 10 ], [ 8, 11 ] ] ]
58-->47:[ ( 2,10, 4)( 3,12, 7)( 5, 9, 8, 6,11), [ [ 3 ], [ 6 ], [ 9 ], [ 7, 10 ], [ 8, 11 ], [ 1, 4 ], [ 2, 5 ] ] ]
58-->46:[ ( 2, 6, 7, 3, 5, 8, 9,10, 4), [ [ 3 ], [ 6 ], [ 9 ], [ 1, 2 ], [ 4, 5 ], [ 7, 8 ], [ 10, 11 ] ] ]
58-->44:[ ( 2, 3, 4), [ [ 3 ], [ 1 ], [ 2 ], [ 4 ], [ 5 ], [ 6, 7, 8 ], [ 9, 10, 11 ] ] ]
58-->42:[ ( 2, 6, 9, 3, 5, 7)( 4, 8)(10,12), [ [ 6 ], [ 8 ], [ 7 ], [ 2 ], [ 1 ], [ 3, 4, 5 ], [ 9, 10, 11 ] ] ]
58-->37:[ ( 2, 6, 8,11,10, 4)( 3, 5, 7), [ [ 3 ], [ 6, 9 ], [ 1, 2 ], [ 4, 5 ], [ 8, 10 ], [ 7, 11 ] ] ]
59-->54:[ ( 2, 4)( 5, 6)( 8, 9,11,10), [ [ 3 ], [ 2 ], [ 1 ], [ 5 ], [ 4 ], [ 6, 9 ], [ 7, 10 ], [ 8, 11 ] ] ]
59-->48:[ ( 2, 5, 6, 8, 9,11,10, 4)( 3, 7), [ [ 3 ], [ 6 ], [ 9 ], [ 1, 4 ], [ 2, 5 ], [ 7, 10 ], [ 8, 11 ] ] ]
59-->46:[ ( 2, 5, 7, 3, 6, 8, 9,10, 4), [ [ 3 ], [ 6 ], [ 9 ], [ 1, 2 ], [ 4, 5 ], [ 7, 8 ], [ 10, 11 ] ] ]
59-->44:[ ( 2, 4)( 5, 6)( 7, 8)(10,11), [ [ 3 ], [ 2 ], [ 1 ], [ 5 ], [ 4 ], [ 6, 7, 8 ], [ 9, 10, 11 ] ] ]
59-->39:[ ( 2, 6, 8,11,10, 4)( 3, 5, 7), [ [ 3 ], [ 6, 9 ], [ 1, 2 ], [ 4, 5 ], [ 8, 10 ], [ 7, 11 ] ] ]

Order 13: Group: No. 6.
Fusions13 := [ [ 1, [ ] ], [ 2, [ 1 ] ], [ 3, [ 1 ] ], [ 4, [ 2 ] ], [ 5, [ 2, 3 ] ], [ 6, [ 4, 5 ] ] ];
Explicit Fusions:
4-->2:[ [ [ 1, 2 ], [ 3, 4 ] ], ( 2, 6, 7, 3)( 8,12)( 9,10) ]
5-->3:[ [ [ 1, 5 ], [ 2, 3 ], [ 4, 6 ] ], ( 2, 9, 7, 6, 4,13)( 3,12,11)( 5, 8) ]
5-->2:[ [ [ 1, 3, 4 ], [ 2, 5, 6 ] ], ( 2, 8,10,11, 4, 6, 3)( 5, 7, 9,13,12) ]
6-->5:[ [ [ 1, 12 ], [ 2, 11 ], [ 3, 10 ], [ 4, 9 ], [ 5, 8 ], [ 6, 7 ] ], ( 2,13, 7, 4,12, 8,10, 9, 5, 3)( 6,11) ]
6-->4:[ [ [ 4, 10, 12 ], [ 1, 3, 9 ], [ 2, 5, 6 ], [ 7, 8, 11 ] ], ( 2,13, 8, 3, 5, 4,11,12, 9, 6,10, 7) ]

Order 14: Groups: Nos. 15, 16.
Fusions14 := [ [ 1, [ ] ], [ 2, [ 1 ] ], [ 3, [ 1 ] ], [ 4, [ 2, 3 ] ], [ 5, [ 2 ] ], [ 6, [ 3 ] ], [ 7, [ 3 ] ], [ 8, [ 2 ] ], [ 9, [ 3 ] ], [ 10, [ 4, 6, 7 ] ], [ 11, [ 4, 5, 6 ] ], [ 12, [ 6, 9 ] ], [ 13, [ 4, 8, 9 ] ], [ 14, [ 5, 8 ] ], [ 15, [ 10, 12, 13 ] ], [ 16, [ 11, 12, 13, 14 ] ] ];
Explicit Fusions:
4-->3:[ [ [ 1, 3 ], [ 2 ] ], ( 2, 3, 4, 5, 6, 7, 8) ]
4-->2:[ [ [ 1 ], [ 2, 3 ] ], ( 4, 9, 6,10,12,13, 8,11, 7, 5) ]
5-->2:[ [ [ 1 ], [ 2, 3 ] ], () ]
6-->3:[ [ [ 1, 2 ], [ 3 ] ], () ]
7-->3:[ [ [ 1, 2 ], [ 3 ] ], ( 2, 9, 3,10, 4,11, 5,12, 6,13, 7,14, 8) ]
8-->2:[ [ [ 1 ], [ 2, 3, 4 ] ], () ]
9-->3:[ [ [ 1, 2, 3 ], [ 4 ] ], () ]
10-->7:[ [ [ 1, 2 ], [ 3 ], [ 4, 5 ] ], ( 2, 6, 3, 7, 4, 8)( 9,10,13,12,14,11) ]
10-->6:[ [ [ 1, 2, 3 ], [ 4 ], [ 5 ] ], ( 2,13, 5,10, 4,14)( 3,12, 7,11) ( 6, 9, 8) ]
10-->4:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ] ], ( 3,11, 5,13, 4,10, 7,14)( 6, 9) ( 8,12) ]
11-->6:[ [ [ 1, 4, 5 ], [ 2 ], [ 3 ] ], ( 2, 3, 4, 5, 6, 7, 8) ]
11-->5:[ [ [ 1 ], [ 2, 4 ], [ 3, 5 ] ], ( 4, 9, 6,10,12,13, 8,11, 7, 5) ]
11-->4:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ] ], () ]
12-->9:[ [ [ 1, 2 ], [ 3, 4 ], [ 5, 6 ], [ 7 ] ], ( 2, 7, 4, 3, 6, 5)( 9,14,11,10,13,12) ]
12-->6:[ [ [ 1, 4, 5 ], [ 2, 3, 6 ], [ 7 ] ], ( 2, 3, 4, 7)( 5, 6)( 9,10,11,14)(12,13) ]
13-->9:[ [ [ 1, 3, 5, 7 ], [ 2 ], [ 4 ], [ 6 ] ], ( 2, 3, 4, 7,12,10, 6,11, 9, 5, 8) ]
13-->8:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ], [ 6, 7 ] ], ( 4, 5)( 8, 9)(12,13) ]
13-->4:[ [ [ 1 ], [ 2, 4, 6 ], [ 3, 5, 7 ] ], ( 5, 7,11, 9)( 6, 8,12,10) ]
14-->8:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ], [ 6, 7 ] ], ( 3, 7,13, 5, 9,11)( 4, 8,14, 6,10,12) ]
14-->5:[ [ [ 1 ], [ 2, 5, 6 ], [ 3, 4, 7 ] ], ( 3, 5, 7,13)( 4, 6, 8,14)( 9,11)(10,12) ]
15-->13:[ [ [ 7 ], [ 1, 6 ], [ 8, 13 ], [ 2, 5 ], [ 9, 12 ], [ 3, 4 ], [ 10, 11 ] ], ( 2, 8, 6, 9,13,12, 5,14,11, 4, 7, 3) ]
15-->12:[ [ [ 1 ], [ 6 ], [ 5 ], [ 2 ], [ 4 ], [ 3 ], [ 7, 8, 9, 10, 11, 12, 13 ] ], ( 3, 7, 4, 6, 5)(10,14,11,13,12) ]
15-->10:[ [ [ 7 ], [ 8, 9, 11 ], [ 10, 12, 13 ], [ 1, 2, 4 ], [ 3, 5, 6 ] ], ( 2, 8,14, 6,11, 5,12, 7,13, 4,10, 3, 9) ]
16-->14:[ [ [ 7 ], [ 6, 13 ], [ 1, 8 ], [ 2, 9 ], [ 5, 12 ], [ 3, 10 ], [ 4, 11 ] ], ( 2, 8,10, 6)( 3, 7)( 4,14,12)( 5, 9,13) ]
16-->13:[ [ [ 7 ], [ 1, 6 ], [ 8, 13 ], [ 2, 5 ], [ 9, 12 ], [ 3, 4 ], [ 10, 11 ] ], ( 2, 8, 3, 7, 6, 9,13,12, 4)( 5,14,11) ]
16-->12:[ [ [ 6 ], [ 1 ], [ 2 ], [ 5 ], [ 3 ], [ 4 ], [ 7, 8, 9, 10, 11, 12, 13 ] ], ( 2, 7, 5, 6, 4, 3)( 9,14,12,13,11,10) ]
16-->11:[ [ [ 7 ], [ 3, 5, 6 ], [ 1, 2, 4 ], [ 10, 12, 13 ], [ 8, 9, 11 ] ], ( 2, 8)( 3, 7)( 4, 6, 5)( 9,14)(10,13) ]

Order 15: Groups: No. 25. NonSchurian Scheme: No. 5
[ [ 1, [ ] ], [ 2, [ 1 ] ], [ 3, [ 1 ] ], [ 4, [ 1 ] ], [ 5, [ 1 ] ], [ 6, [ 2 ] ], [ 7, [ 3 ] ], [ 8, [ 2, 3 ] ], [ 9, [ 2, 4 ] ], [ 10, [ 2 ] ], [ 11, [ 3 ] ], [ 12, [ 6, 10 ] ], [ 13, [ 7, 11 ] ], [ 14, [ 8 ] ], [ 15, [ 7 ] ], [ 16, [ 6, 9 ] ], [ 17, [ 6, 8, 11 ] ], [ 18, [ 7, 8, 10 ] ], [ 19, [ 10 ] ], [ 20, [ 13, 15 ] ], [ 21, [ 12, 19 ] ], [ 22, [ 18 ] ], [ 23, [ 12, 13, 14, 17, 18 ] ], [ 24, [ 15, 18, 19 ] ], [ 25, [ 20, 21, 22, 23, 24 ] ] ]

Explicit Fusions:
6-->2:[ [ [ 1, 2 ], [ 3 ] ], () ]
7-->3:[ [ [ 1, 2 ], [ 3 ] ], () ]
8-->3:[ [ [ 1, 3 ], [ 2 ] ], ( 2, 4, 6)( 3, 5, 7, 8, 9,10,11) ]
8-->2:[ [ [ 1 ], [ 2, 3 ] ], ( 5, 8, 9,13, 7)( 6,12,14,11,10) ]
9-->4:[ [ [ 1, 2 ], [ 3 ] ], ( 2, 5, 7)( 3, 4, 6)( 8,15,13)( 9,14,12)(10,11)]
9-->2:[ [ [ 1 ], [ 2, 3 ] ], ( 5, 8,10, 6,12,15,13, 7)( 9,14,11) ]
10-->2:[ [ [ 1 ], [ 2, 3 ] ], () ]
11-->3:[ [ [ 1 ], [ 2, 3 ] ], () ]
12-->10:[ [ [ 1, 2 ], [ 3 ], [ 4 ] ], () ]
12-->6:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], () ]
13-->11:[ [ [ 1, 2 ], [ 3 ], [ 4 ] ], () ]
13-->7:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], () ]
14-->8:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], ( 2, 3)( 4, 7)( 8,14)( 9,11,10,15,12) ]
15-->7:[ [ [ 1, 2 ], [ 3, 4 ], [ 5 ] ], ( 4, 5)( 9,10)(14,15) ]
16-->9:[ [ [ 1, 2 ], [ 3 ], [ 4, 5 ] ], ( 2, 3)( 4, 7, 5, 6)( 8, 9)(10,11)(12,14,13,15) ]
16-->6:[ [ [ 1 ], [ 2 ], [ 3, 4, 5 ] ], ( 5, 8,10, 6,12,13, 7)( 9,15,14)]
17-->11:[ [ [ 1, 5 ], [ 2, 4 ], [ 3 ] ],( 2, 4, 6)( 3, 5, 7,12, 8,13, 9,14,10,15,11) ]
17-->8:[ [ [ 1, 2 ], [ 3 ], [ 4, 5 ] ], ( 2, 3)( 4, 7)( 8,11)(12,15) ]
17-->6:[ [ [ 1 ], [ 2 ], [ 3, 4, 5 ] ], ( 2, 3)( 4,15)( 5, 7,14,12, 9,10,13, 8, 6,11) ]
18-->10:[ [ [ 1 ], [ 2, 4 ], [ 3, 5 ] ], ( 5, 8, 9,11,12,14,13, 7)( 6,10)]
18-->8:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ] ], (10,12)(11,13) ]
18-->7:[ [ [ 1, 4, 5 ], [ 2 ], [ 3 ] ],( 2, 4, 6)( 3, 5, 7, 8, 9,12,10,13,11) ]
19-->10:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ] ], (10,13)(11,14)(12,15) ]
20-->15:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5, 6 ] ], () ]
20-->13:[ [ [ 1, 2 ], [ 3, 4 ], [ 5 ], [ 6 ] ], ( 4, 5)( 9,10)(12,13) ]
21-->19:[ [ [ 1, 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ] ], () ]
21-->12:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5, 6 ] ], (10,13)(11,14)(12,15) ]
22-->18:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5 ], [ 6, 7 ] ], ( 4,10,13, 8,14, 9,12, 6, 5,11,15, 7) ]
23-->18:[ [ [ 1, 2 ], [ 3 ], [ 4 ], [ 5, 6 ], [ 7, 8 ] ],( 4, 6, 5, 7)( 8,14, 9,15)(10,12,11,13) ]
23-->17:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5, 7 ], [ 6, 8 ] ], (10,12)(11,13)]
23-->14:[ [ [ 1, 2 ], [ 3, 4 ], [ 5, 8 ], [ 6, 7 ] ],( 2, 3)( 4, 6)( 5, 7)(10,14,11,15) ]
23-->13:[ [ [ 1, 6, 8 ], [ 2, 5, 7 ], [ 3 ], [ 4 ] ],( 2, 4, 6)( 3, 5, 7,10,15,13, 9,14,12, 8,11) ]
23-->12:[ [ [ 1 ], [ 2 ], [ 3, 5, 6 ], [ 4, 7, 8 ] ],( 2, 3)( 4,14, 8,15,10,11, 5, 6,12, 9, 7,13) ]
24-->19:[ [ [ 1, 7 ], [ 2, 6 ], [ 3, 8 ], [ 4, 9 ], [ 5 ] ],( 2, 6,11,12,13, 5,10, 4)( 3, 7) ]
24-->18:[ [ [ 1, 2 ], [ 3, 4 ], [ 5 ], [ 6, 7 ], [ 8, 9 ] ],( 2, 6, 5, 3, 7, 4)( 8,10,11, 9)(12,14,15,13) ]
24-->15:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5, 6, 7, 8, 9 ] ],( 7,10,14,13, 9,12,11) ]
25-->24:[ ( 2, 3, 4, 5)( 7, 8,12, 9,14,15,11), [ [ 4 ], [ 1 ], [ 2 ], [ 3 ], [ 5, 10 ], [ 6, 11 ], [ 9, 14 ], [ 7, 12 ], [ 8, 13 ] ] ]
25-->23:[ ( 2, 5, 4, 6, 3, 7, 9,12,11)( 8,13,15,10), [ [ 10 ], [ 5 ], [ 1, 4 ], [ 2, 3 ], [ 6, 9 ], [ 11, 14 ], [ 7, 8 ], [ 12, 13 ] ] ]
25-->22:[ ( 2, 5, 4,10, 7, 9,13,12, 6, 3,11)( 8,15), [ [ 5, 10 ], [ 1, 4 ], [ 9, 11 ], [ 6, 14 ], [ 2, 3 ], [ 8, 12 ], [ 7, 13 ] ] ]
25-->21:[ ( 2, 9,13,11)( 3,10, 5, 6)( 4,14,15)( 7, 8,12), [ [ 10 ], [ 5 ], [ 4, 9, 14 ], [ 1, 6, 11 ], [ 2, 7, 12 ], [ 3, 8, 13 ] ] ]
25-->20:[ ( 2, 3, 4, 5)( 6, 9)( 7,10, 8)(11,12), [ [ 4 ], [ 1 ], [ 2 ], [ 3 ], [ 5, 6, 7, 8, 9 ], [ 10, 11, 12, 13, 14 ] ] ]

Order 16: Groups: Nos. 209 to 222.
Fusions16:=[ [1,[]],[2,[1]],[3,[1]],[4,[1]],[5,[]],[6,[]],[7,[]],[8,[2,3]],[9,[2,7]],[10,[2,7]],[11,[2]], [12,[3,5]],[13,[3,7]],[14,[5]],[15,[3,6]],[16,[3,5]],[17,[3]],[18,[3]],[19,[3]],[20,[4]],[21,[4]],[22,[8]],[23,[8]],[24,[8,9,13]],[25,[[8]],[27,[8]],[28,[9,13]],[29,[9]],[30,[4,9]],[31,[9]],[32,[12,14]],[33,[6,12,16]],[34,[15]],[35,[13]],[36,[13]],[37,[22,24]],[38,[23,24]],[39,[10,22,25]],[40,[22,26]],[41,[23,25]],[42,[23,26]],[43,[24]],[44,[24]],[45,[24]],[46,[24]],[47,[4,12,25,28]],[48,[25]],[49,[25,29]],[50,[25,29]],[51,[25]],[52,[24,35]],[53,[24]],[54,[5,24,30]],[55,[6,24,30]],[56,[24,36]],[57,[24]],[58,[24,31]],[59,[24,31]],[60,[10,28,35]],[61,[28,36]],[62,[32]],[63,[18,34]],[64,[28,37,43]],[65,[37,45]],[66,[38,43]],[67,[38,45]],[68,[37,52]],[69,[37,53]],[70,[37,56]],[71,[37,57]],[72,[38,52]],[73,[38,53]],[74,[38,56]],[75,[38,57]],[76,[25,43,52]],[77,[14,43,54]],[78,[15,16,43,54,55]],[79,[17,43,55]],[80,[44,52]],[81,[44,53]],[82,[43,56]],[83,[43,58]],[84,[43,58,59]],[85,[43,59]],[86,[44,56]],[87,[44,57]],[88,[45,52]],[89,[45,54]],[90,[45,55]],[91,[46,52]],[92,[53,46]],[93,[45,56]],[94,[18,45,58]],[95,[45,59]],[96,[46,56]],[97,[46,57]],[98,[64,68,76]],[99,[39,60,64,76]],[100,[64,69]],[101,[64,70,82]],[102,[61,64,82]],[103,[64,71]],[104,[65,68,88]],[105,[65,69]],[106,[65,70,93]],[107,[65,71]],[108,[66,72,76]],[109,[41,66,76]],[110,[66,74,82]],[111,[66,82]],[112,[67,72,88]],[113,[67,74,93]],[114,[30,39,47,60]],[115,[30,39,48,50]],[116,[39,40,49,51]],[117,[31,41,47,61]],[118,[41,48,49]],[119,[11,27,31,41,50,51]],[120,[76,80]],[121,[76,91]],[122,[80,88]],[123,[88,91]],[124,[64]],[125,[44,64,66]],[126,[64,65,66]],[127,[29,46,66]],[128,[44,46,67]],[129,[47,54,98]],[130,[98,104]],[131,[58,104]],[132,[54,58,70]],[133,[76]],[134,[81]],[135,[53,76,88]],[136,[76,82,88]],[137,[81]],[138,[26,57,88]],[139,[53,57,93]],[140,[98,99,124]],[141,[101,102,124]],[142,[98,99,109,125]],[143,[80,99,108,125]],[144,[101,102,111,125]],[145,[86,102,110,125]],[146,[98,104,109,126]],[147,[99,108,109,126]],[148,[101,106,111,126]],[149,[102,110,111,126]],[150,[91,108,109,127]],[151,[80,91,112,128]],[152,[96,110,111,127]],[153,[86,96,113,128]],[154,[98,99,133]],[155,[20,32,77,129]],[156,[21,33,78,129]],[157,[99,100,120]],[158,[69,98,104,135]],[159,[99,135]],[160,[89,129,130]],[161,[48,99,120,121]],[162,[98,102,104,136]],[163,[99,101,102,136]],[164,[83,130,131]],[165,[84,130,131]],[166,[99,103,121]],[167,[77,83,101,132]],[168,[78,84,101,132]],[169,[100,102,103]],[170,[40,71,104,138]],[171,[69,71,106,139]],[172,[94,131]],[173,[18,89,106,132]],[174,[108,109,133]],[175,[78,109,120]],[176,[73,108,112,135]],[177,[109,135]],[178,[109,120,121]],[179,[108,111,112,136]],[180,[109,110,111,136]],[181,[51,84,109,121]],[182,[34,78,84,111]],[183,42,75,112,138]],[184,[73,75,113,139]],[185,[114,129,140,154]],[186,[129,130,140,158,159]],[187,[130,140,141,162,163]],[188,[120,142,143,154,174]],[189,[142,158,159,177]],[190,[120,122,143,159,176]],[191,[142,144,145,162,163,180]],[192,[122,143,144,163,179]],[193,[130,146,147,154,174]],[194,[100,105,129,130,146,158]],[195,[130,131,146,158,177]],[196,[147,159,176,177]],[197,[117,129,130,131,146,162]],[198,[131,146,149,162,180]],[199,[147,148,149,163,179,180]],[200,[103,107,130,131,146,170]],[201,[100,103,105,107148,171]],[202,[49,121,151,176]],[203,[81,92,120,121,151,176]],[204,[50,121,123,150,176,177]],[205,[120,121,122,123,151,177]],[206.[180,179,152,150]],[207,[87,97,122,123,151,183]],[208,[184,153,97,81]],[209,[87,92,134,137,153,184,208]],[210,[165,172,182,197,198]],[211,[155,160,164,165,167,186,187,194,195,197]],[212,135,160,164,172,194,195,197,198,200]],[213,[157,166,169,178,199,201,205]],[214,[205,199,182,181,175,168,161]],[215,[203,190,161,157,135,134,125,108]],[216,[204,203,190,178,175,166,161,128,125,115,112]],[217,[204,203,181,178,137,128,127,119,112]],[218,[147,160,164,185,187,193,197]],[219,[194,193,188,186,185,175,160,157,156]],[220,[202,200,193,181,166,165]],[221,[161,178,188,193,202]],[222,[185,155,133,62]]];

Explicit Fusions:
8-->3:[ [ [ 1, 2 ], [ 3 ] ], () ]
8-->2:[ [ [ 1 ], [ 2, 3 ] ], () ]
9-->7:[ [ [ 1, 2 ], [ 3 ] ], () ]
9-->2:[ [ [ 1 ], [ 2, 3 ] ], () ]
10-->7:[ ( 2, 3, 4, 5, 6, 7, 8, 9), [ [ 2 ], [ 1, 3 ] ] ]
10-->2:[ [ [ 1 ], [ 2, 3 ] ], ( 4,10,13, 8,12,14,15, 9, 6,11, 7, 5) ]
11-->2:[ [ [ 1 ], [ 2, 3 ] ], ( 4,10,15, 9, 6,14,12,13, 8,16,11, 7, 5) ]
12-->5:[ [ [ 1, 2 ], [ 3 ] ], () ]
12-->3:[ ( 2, 5)( 3, 6, 8,10,11,12,13, 4, 7, 9), [ [ 2 ], [ 1, 3 ] ] ]
13-->7:[ [ [ 1, 2 ], [ 3 ] ], () ]
13-->3:[ [ [ 1 ], [ 2, 3 ] ], () ]
14-->5:[ ( 2, 8, 3, 6, 5, 7, 9,11,12)( 4,10,16)(13,14,15), [ [ 2 ], [ 1, 3 ] ] ]
14-->3:[ [ [ 1 ], [ 2, 3 ] ], ( 7,15,11,13, 9)( 8,16,12,14,10) ]
15-->6:[ ( 2, 5,10)( 3, 7, 6, 8,11,15,14,16,12)( 4, 9,13), [ [ 2 ], [ 1, 3 ] ] ]
AS 15-->3:[ [ [ 1 ], [ 2, 3 ] ], ( 7,15,11,13, 9)( 8,16,12,14,10) ]
16-->5:[ ( 2,13, 8, 3,12, 4,16)( 5,14,10, 9, 6,11)( 7,15), [ [ 3 ], [ 1, 2 ] ] ]
16-->3:[ [ [ 1 ], [ 2, 3 ] ], ( 7,15,11,12,14,10, 9)( 8,16,13) ]
17-->3:[ [ [ 1 ], [ 2, 3 ] ], ( 7,15,12,14, 9)( 8,16,13) ]
18-->3:[ [ [ 1 ], [ 2, 3 ] ], ( 7,15,11,13, 9)( 8,16,12,14,10) ]
19-->3:[ [ [ 1 ], [ 2, 3 ] ], ( 7,15,11,12,14,10, 9)( 8,16,13) ]
20-->4:[ ( 2,10,16, 4, 8,13,15, 3, 9, 5, 7)( 6,11), [ [ 2 ], [ 1, 3 ] ] ]
21-->4:[ ( 2,10,16, 4, 8, 6,11,13,15, 3, 9,12, 5, 7), [ [ 2 ], [ 1, 3 ] ] ]
22-->8:[ ( 2, 3)( 6, 7)(10,11)(14,15), [ [ 2 ], [ 1, 3 ], [ 4 ] ] ]
23-->8:[ [ [ 1 ], [ 2, 3 ], [ 4 ] ], () ]
24-->13:[ [ [ 1, 2 ], [ 3 ], [ 4 ] ], () ]
24-->9:[ [ [ 1 ], [ 2, 3 ], [ 4 ] ], () ]
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218-->185:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8, 9 ], [ 10, 11 ], [ 12, 13 ], [ 14, 15 ] ], () ]
218-->164:[ ( 9,12,10)(13,16,15,14), [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ], [ 6, 7 ], [ 9, 11 ], [ 8, 10 ], [ 13, 14 ], [ 12, 15 ] ] ]
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219-->160:[ (10,12,11)(13,16,15,14), [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ], [ 6, 7 ], [ 8, 10 ], [ 9, 11 ], [ 13, 14 ], [ 12, 15 ] ] ]
219-->157:[ ( 5, 9,10,11,14)( 6,12,15, 8,16, 7,13), [ [ 1 ], [ 2 ], [ 3 ], [ 12, 13 ], [ 14, 15 ], [ 4, 8 ], [ 5, 9 ], [ 6, 10 ], [ 7, 11 ] ] ]
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220-->200:[ ( 5, 6)( 7, 8)( 9,11,12,10)(14,15), [ [ 1 ], [ 2 ], [ 3 ], [ 5 ], [ 4 ], [ 7 ], [ 6 ], [ 9, 11 ], [ 8, 10 ], [ 12, 14 ], [ 13, 15 ] ] ]
220-->193:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8, 9 ], [ 10, 11 ], [ 12, 13 ], [ 14, 15 ] ], () ]
220-->181:[ ( 3, 7, 5, 4, 8, 6)( 9,12,14,16,10)(11,15), [ [ 1 ], [ 5 ], [ 4 ], [ 6, 7 ], [ 2, 3 ], [ 9, 15 ], [ 8, 14 ], [ 11, 12 ], [ 10, 13 ] ] ]
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220-->165:[ ( 5, 6)( 7, 8)( 9,12,10)(13,14,15,16), [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ], [ 6, 7 ], [ 9, 11 ], [ 8, 10 ], [ 12, 15 ], [ 13, 14 ] ] ]
221-->202:[ ( 3,10,14, 7)( 4, 9,13, 8)( 5,11)( 6,12), [ [ 1 ], [ 6 ], [ 7 ], [ 10 ], [ 11 ], [ 13 ], [ 12 ], [ 2, 3 ], [ 4, 5 ], [ 8, 9 ], [ 14, 15 ] ] ]
221-->193:[ ( 3, 8, 5)( 4, 7, 6)(11,16,13)(12,15,14), [ [ 1 ], [ 4 ], [ 5 ], [ 7 ], [ 6 ], [ 3 ], [ 2 ], [ 8, 9 ], [ 12, 13 ], [ 14, 15 ], [ 10, 11 ] ] ]
221-->188:[ ( 3,12,15,13, 8, 9, 5)( 4,11,16,14, 7,10, 6), [ [ 1 ], [ 4 ], [ 5 ], [ 8 ], [ 9 ], [ 13 ], [ 12 ], [ 6, 7 ], [ 2, 3 ], [ 14, 15 ], [ 10, 11 ] ] ]
221-->178:[ ( 3, 4)( 5, 7)( 6, 8)(10,12,16,11,13,15), [ [ 1 ], [ 3 ], [ 2 ], [ 6, 7 ], [ 4, 5 ], [ 8, 14 ], [ 9, 15 ], [ 10, 13 ], [ 11, 12 ] ] ]
221-->161:[ ( 3, 8, 5)( 4, 7, 6)(10,12,15,11,14,13,16), [ [ 1 ], [ 4 ], [ 5 ], [ 6, 7 ], [ 2, 3 ], [ 8, 15 ], [ 9, 14 ], [ 10, 13 ], [ 11, 12 ] ] ]
# The case of No. 222, the elementary abelian group of order 16, is tedious because the "IsomorphicSubgroup" command often fails. Several cases were ruled out by hand with ad hoc group theoretic conditions.
222-->185:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8, 9 ], [ 10, 11 ], [ 12, 13 ], [ 14, 15 ] ], () ]
222-->155:[ (10,12,11)(14,16), [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ], [ 6, 7 ], [ 8, 10 ], [ 9, 11 ], [ 12, 15 ], [ 13, 14 ] ] ]
222-->133:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ], [ 6, 7 ], [ 8, 9 ], [ 10, 11 ], [ 12, 13 ], [ 14, 15 ] ], () ]
222-->62:[ (6,8,16,12,10,11,15,9)(7,13), [ [ 1, 2, 3 ], [ 4, 8, 12 ], [ 5, 11, 14 ], [ 6, 9, 15 ], [ 7, 10, 13 ] ] ]

Order 17: Group: No. 5.
Fusions17:=[ [ 1, [ ] ], [ 2, [ 1 ] ], [ 3, [ 2 ] ], [ 4, [ 3 ] ], [ 5, [ 4 ] ] ];

Explicit Fusions:
3-->2:[ [ [ 1, 3 ], [ 2, 4 ] ], ( 2,11,14, 8,12, 6, 4, 3,10,16, 9,13,17, 7) ]
4-->3:[ [ [ 1, 4 ], [ 2, 8 ], [ 3, 5 ], [ 6, 7 ] ], ( 2, 4,16,10, 8,12)( 3,17, 7,15, 6,13)( 9,14,11) ]
5-->4:[ ( 2, 3, 5, 9,17)( 4, 7,13,10,16)( 6,11,14, 8,15), [ [ 1, 16 ], [ 2, 15 ], [ 3, 14 ], [ 4, 13 ], [ 5, 12 ], [ 6, 11 ], [ 7, 10 ], [ 8, 9 ] ] ]

Order 18: Groups: Nos. 91 to 95.
Fusions18:=[[1,[]],[2,[1]],[3,[1]],[4,[1]],[5,[1]],[6,[3]],[7,[2,4]],[8,[2]],[9,[2,5]],[10,[3,4]],[11,[3,4]],[12,[3,5]],[13,[5]],[14,[4]],[15,[6,10]],[16,[6,12]],[17,[7,10]],[18,[7]],[19,[7,8]],[20,[7,14]],[21,[12,13]],[22,[12]],[23,[10,12]],[24,[12]],[25,[10,14]],[26,[16,22]],[27,[15,16,23]],[28,[15,25]],[29,[6,11,14]],[30,[11,17,19]],[31,[9,17,23]],[32,[17,20,25]],[33,[18,20]],[34,[19]],[35,[7]],[36,[8,9,13]],[37,[9,13]],[38,[21]],[39,[12]],[40,[11,21,23]],[41,[22,24]],[42,[15,17]],[43,[15,17,18]],[44,[16,21,22]],[45,[16,24]],[46,[16,24]],[47,[30,34]],[48,[17,35]],[49,[18,19,20]],[50,[38,40]],[51,[23,39]],[52,[22,23]],[53,[22,23,25]],[54,[27,31,42]],[55,[28,32,42]],[56,[27,31,43]],[57,[28,32,33,43]],[58,[27,40,44]],[59,[26,27,52]],[60,[26,41,45]],[61,[26,27,28,53]],[62,[26,46]],[63,[30,31,36,40]],[64,[21,36]],[65,[30,32,49]],[66,[31,52]],[67,[31,32,53]],[68,[29,30,43,49]],[69,[40,44,52]],[70,[29,40,44,53]],[71,[26,38,44]],[72,[26,39]],[73,[54,59,66]],[74,[54,55,61,67]],[75,[56,59,66]],[76,[56,57,61,67]],[77,[47,50,63]],[78,[31,48,51]],[79,[50,63,64]],[80,[37,38,64]],[81,[33,34,49]],[82,[33,35]],[83,[50,58,59,69,71]],[84,[51,59,72]],[85,[50,58,61,70,71]],[86,[51,61,72]],[87,[45,54,58,63,66]],[88,[56,58,63,65,67,68,70]],[89,[47,57,65,68,81]],[90,[48,57,82]],[91,[73,78,84]],[92,[76,78,86,90]],[93,[60,74,75,79,83,85,87,88]],[94,[87,83,77,73,60]],[95,[89,88,85,77,76]] ];

Explicit Fusions:
6-->3:[ [ [ 1, 2 ], [ 3 ] ], () ]
7-->4:[ [ [ 1, 2 ], [ 3 ] ], () ]
7-->2:[ [ [ 1 ], [ 2, 3 ] ], () ]
8-->2:[ [ [ 1 ], [ 2, 3 ] ], () ]
9-->5:[ ( 2, 3, 4, 5, 6, 7, 8, 9,10), [ [ 2 ], [ 1, 3 ] ] ]
9-->2:[ [ [ 1 ], [ 2, 3 ] ], ( 4,11, 7, 5)( 6,12,15, 9)( 8,13)(10,14,16,17) ]
10-->4:[ [ [ 1, 2 ], [ 3 ] ], () ]
10-->3:[ [ [ 1 ], [ 2, 3 ] ], () ]
11-->4:[ ( 2, 4, 6, 8, 9,10,11,12,13, 3, 5, 7), [ [ 2 ], [ 1, 3 ] ] ]
11-->3:[ [ [ 1 ], [ 2, 3 ] ], ( 5, 9,15,17,13, 7)( 6,14,12,16, 8,10) ]
12-->5:[ [ [ 1, 2 ], [ 3 ] ], () ]
12-->3:[ [ [ 1 ], [ 2, 3 ] ], () ]
13-->5:[ [ [ 1, 2 ], [ 3 ] ], () ]
14-->4:[ [ [ 1 ], [ 2, 3 ] ], () ]
15-->10:[ [ [ 1, 2 ], [ 3 ], [ 4 ] ], () ]
15-->6:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], () ]
16-->12:[ [ [ 1, 2 ], [ 3 ], [ 4 ] ], () ]
16-->6:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], () ]
17-->10:[ ( 2, 3, 4)( 8, 9,10)(14,15,16), [ [ 2 ], [ 1, 3 ], [ 4 ] ] ]
17-->7:[ [ [ 1 ], [ 2, 3 ], [ 4 ] ], ( 4, 5)(10,11)(16,17) ]
18-->7:[ [ [ 1 ], [ 2, 3 ], [ 4 ] ], () ]
19-->8:[ [ [ 1 ], [ 2, 3 ], [ 4 ] ], () ]
19-->7:[ ( 3, 7)( 4, 8)( 5, 9,11,13)( 6,10,12,14), [ [ 1 ], [ 3 ], [ 2, 4 ] ] ]
20-->14:[ [ [ 1, 2 ], [ 3 ], [ 4 ] ], () ]
20-->7:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], () ]
21-->13:[ [ [ 1, 2 ], [ 3 ], [ 4 ] ], () ]
21-->12:[ ( 2, 4)( 3, 5, 6, 7)(11,13)(12,14,15,16), [ [ 2 ], [ 1, 3 ], [ 4 ] ] ]
22-->12:[ [ [ 1 ], [ 2, 3 ], [ 4 ] ], () ]
23-->12:[ ( 4, 7,10)( 5, 8,11)( 6, 9,12), [ [ 1 ], [ 3 ], [ 2, 4 ] ] ]
23-->10:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], (10,13)(11,14)(12,15) ]
24-->12:[ ( 4,13, 5,16, 6,17, 9,18,12,10)( 7,14, 8,15,11), [ [ 1 ], [ 4 ], [ 2, 3 ] ] ]
25-->14:[ [ [ 1, 2 ], [ 3 ], [ 4 ] ], () ]
25-->10:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], () ]
26-->22:[ [ [ 1, 2 ], [ 3 ], [ 4 ], [ 5 ] ], () ]
26-->16:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5 ] ], () ]
27-->23:[ [ [ 1, 2 ], [ 3 ], [ 4 ], [ 5 ] ], () ]
27-->16:[ ( 4, 7,10)( 5, 8,11)( 6, 9,12), [ [ 1 ], [ 2 ], [ 4 ], [ 3, 5 ] ] ]
27-->15:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], (10,13)(11,14)(12,15) ]
28-->25:[ [ [ 1, 2 ], [ 3 ], [ 4 ], [ 5 ] ], () ]
28-->15:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], () ]
29-->14:[ ( 2, 4, 6, 8,14, 9,15,10,16,11,17,12,18,13, 3, 5, 7), [ [ 3 ], [ 1, 5 ], [ 2, 4 ] ] ]
29-->11:[ [ [ 1, 2 ], [ 3 ], [ 4, 5 ] ], ( 2, 3)( 4, 5, 6, 7, 8)( 9,10,11,12,13)(14,15,16,17,18) ]
29-->6:[ ( 2, 3)( 4,18)( 5, 8, 7,17,14)( 6,13,15,10,16, 9,12,11), [ [ 2 ], [ 1 ], [ 3, 4, 5 ] ] ]
30-->19:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ] ], ( 4, 5) ]
30-->17:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], ( 9,11,12,16,17,14,10,15,13) ]
30-->11:[ ( 2, 3, 4)( 5, 7, 9)( 6, 8,10,11,12,13,14), [ [ 2 ], [ 1, 4 ], [ 3, 5 ] ] ]
31-->23:[ ( 2, 3, 4), [ [ 2 ], [ 1, 3 ], [ 4 ], [ 5 ] ] ]
31-->17:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], ( 8,13,10, 9)(11,14,16,12,15) ]
31-->9:[ [ [ 1 ], [ 2, 4 ], [ 3, 5 ] ], ( 5, 7, 9,11)( 6, 8,10,12) ]
32-->25:[ ( 2, 3, 4)( 8, 9,10)(14,15,16), [ [ 2 ], [ 1, 3 ], [ 4 ], [ 5 ] ] ]
32-->20:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ] ], ( 4, 5)(10,11)(16,17) ]
32-->17:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], () ]
33-->20:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ] ], () ]
33-->18:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], () ]
34-->19:[ ( 3, 9,11, 5, 7,13,15,17)( 4,10,12, 6, 8,14,16,18), [ [ 1 ], [ 3 ], [ 4 ], [ 2, 5 ] ] ]
35-->7:[ [ [ 1 ], [ 2 ], [ 3, 4, 5 ] ], ( 9,13)(10,14)(11,15)(12,16) ]
36-->13:[ ( 2, 3, 4, 5, 6,11, 7,12, 8,13, 9,14,10), [ [ 2 ], [ 4 ], [ 1, 3, 5 ] ] ]
36-->9:[ [ [ 1 ], [ 2, 4 ], [ 3, 5 ] ], ( 7,11)( 8,12)( 9,13)(10,14) ]
36-->8:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ] ], ( 4, 7, 5)( 6, 8, 9)(12,15,13)(14,16,17) ]
37-->13:[ ( 2, 3, 4, 5, 6, 7, 8, 9,10)(11,13,14)(15,18), [ [ 2 ], [ 3 ], [ 1, 4, 5 ] ] ]
37-->9:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ] ], (11,15,14,17,12,18)(13,16) ]
38-->21:[ ( 2, 5, 7, 3, 4, 6, 8)(11,14,16,12,13,15,17), [ [ 2 ], [ 3 ], [ 1, 4 ], [ 5 ] ] ]
39-->12:[ [ [ 1 ], [ 2, 3, 4 ], [ 5 ] ], ( 5, 7)( 6, 8)(14,16)(15,17) ]
40-->23:[ ( 4, 6, 8, 9,11,10, 5, 7), [ [ 1 ], [ 3 ], [ 2, 4 ], [ 5 ] ] ]
40-->21:[ ( 6, 9,12, 8,11, 7,10)(14,16,17,15), [ [ 1 ], [ 2 ], [ 4 ], [ 3, 5 ] ] ]
40-->11:[ ( 2, 4)( 3, 5)(10,11,13,15,12,14), [ [ 2 ], [ 1, 3 ], [ 4, 5 ] ] ]
41-->24:[ ( 7,13)( 8,14,10,16)( 9,15,11,17)(12,18), [ [ 1 ], [ 2 ], [ 5 ], [ 3, 4 ] ] ]
41-->22:[ ( 4, 7,10)( 5, 8,11,13)( 6, 9,12,16)(15,17), [ [ 1 ], [ 3 ], [ 4 ], [ 2, 5 ] ] ]
42-->17:[ ( 2, 3, 6)( 4, 5)( 7,17,11,16, 9,18)( 8,14,12,15)(10,13), [ [ 2 ], [ 4, 5 ], [ 1, 3 ], [ 6 ] ] ]
42-->15:[ ( 2, 5, 3, 6, 4)( 8,11, 9,12,10)(14,17,15,18,16), [ [ 4 ], [ 5 ], [ 1, 2, 3 ], [ 6 ] ] ]
43-->18:[ [ [ 1 ], [ 2, 4 ], [ 3, 5 ], [ 6 ] ], ( 4, 5)(10,11)(16,17) ]
43-->17:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ], [ 6 ] ], () ]
43-->15:[ ( 2, 3, 4)( 8, 9,10)(14,15,16), [ [ 2 ], [ 3 ], [ 1, 4, 5 ], [ 6 ] ] ]
44-->22:[ ( 2, 4)( 3, 5, 8, 6, 9, 7)(11,13)(12,14,17,15,18,16), [ [ 3 ], [ 1, 5 ], [ 2, 4 ], [ 6 ] ] ]
44-->21:[ [ [ 1, 2 ], [ 3 ], [ 4, 5 ], [ 6 ] ], ( 4, 5)( 6, 9)( 7, 8)(13,14)(15,18)(16,17) ]
44-->16:[ ( 2, 3)( 4, 5, 7, 8)( 6, 9)(10,18)(11,14,13,17)(12,16), [ [ 2 ], [ 1 ], [ 3, 4, 5 ], [ 6 ] ] ]
45-->24:[ ( 2, 3)( 4, 7,10)( 5, 9,11, 6, 8,12)(15,18), [ [ 1, 2 ], [ 4 ], [ 3, 5 ], [ 6 ] ] ]
45-->16:[ ( 4,13, 5,16, 6,17, 9,18,12,10)( 7,14, 8,15,11), [ [ 1 ], [ 2 ], [ 6 ], [ 3, 4, 5 ] ] ]
46-->24:[ [ [ 1, 2 ], [ 3 ], [ 4, 5 ], [ 6 ] ], ( 2, 3)( 4, 6)( 7, 9)(10,12)(13,18)(14,16,15,17) ]
46-->16:[ ( 2, 3)( 4,14, 5,15, 8,13,11, 6,18)( 7,17,10,12, 9,16), [ [ 2 ], [ 1 ], [ 6 ], [ 3, 4, 5 ] ] ]
47-->34:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ], [ 6 ] ], ( 4, 5) ]
47-->30:[ ( 3, 4)( 5, 6)( 7,11, 9,13,15,17)( 8,12,10,14,16,18), [ [ 1 ], [ 2 ], [ 3 ], [ 5 ], [ 4, 6 ] ] ]
48-->35:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ], [ 6 ] ], ( 4, 5) ]
48-->17:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5, 6 ] ], ( 9,13)(10,15,11,14)(12,16,17) ]
49-->20:[ ( 3, 7)( 4, 8)( 5, 9,15,11,17,13)( 6,10,16,12,18,14), [ [ 1 ], [ 4 ], [ 2, 6 ], [ 3, 5 ] ] ]
49-->19:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5, 6 ] ], ( 7, 9)( 8,10)(11,17)(12,18)(13,15)(14,16) ]
49-->18:[ ( 3, 5)( 4, 6)( 7,17)( 8,18)(11,13)(12,14), [ [ 1 ], [ 3 ], [ 2 ], [ 4, 5, 6 ] ] ]
50-->40:[ ( 4, 7,10, 9)( 5, 6,11, 8,12)(16,18), [ [ 1 ], [ 3 ], [ 5 ], [ 2, 4 ], [ 6 ] ] ]
50-->38:[ ( 2, 8)( 3, 9)( 4, 5)(10,17,18,16)(11,12,13,15,14), [ [ 4 ], [ 2 ], [ 3 ], [ 1 ], [ 5, 6 ] ] ]
51-->39:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5, 6 ] ], (14,16)(15,17) ]
51-->23:[ ( 4,10, 5,11, 6,12, 9, 8, 7), [ [ 1 ], [ 5 ], [ 2, 3, 4 ], [ 6 ] ] ]
52-->23:[ ( 4, 7,16)( 5, 8,17)( 6, 9,18)(10,13)(11,14)(12,15), [ [ 1 ], [ 3 ], [ 5, 6 ], [ 2, 4 ] ] ]
52-->22:[ ( 4,13, 7,16,10)( 5,14, 8,17,11)( 6,15, 9,18,12), [ [ 1 ], [ 5 ], [ 6 ], [ 2, 3, 4 ] ] ]
53-->25:[ [ [ 1 ], [ 2 ], [ 3, 5 ], [ 4, 6 ] ], (10,13)(11,14)(12,15) ]
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53-->22:[ ( 4, 7,10)( 5, 8,11)( 6, 9,12), [ [ 1 ], [ 3 ], [ 4 ], [ 2, 5, 6 ] ] ]
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54-->31:[ ( 2, 3, 6)( 4, 5)( 7,10)( 8,11)( 9,12)(13,17)(14,16)(15,18), [ [ 2 ], [ 4, 5 ], [ 1, 3 ], [ 6 ], [ 7 ] ] ]
54-->27:[ ( 2, 5, 3, 6, 4), [ [ 4 ], [ 5 ], [ 1, 2, 3 ], [ 6 ], [ 7 ] ] ]
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55-->28:[ ( 2, 5, 3, 6, 4)( 8,11, 9,12,10)(14,17,15,18,16), [ [ 4 ], [ 5 ], [ 1, 2, 3 ], [ 6 ], [ 7 ] ] ]
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#For No. 94, both the algebraic method and partition method have problems for comparing 94 to 53, 20, and 14. These can be ruled out as #possible fusions because such fusions would force No. 61 or 65 to be fusions of No. 94, which they are not.) 94-->87:[ (2,5,15,14,12,4,7,8,16,9,18,13,10)(3,6,17,11),[ [ 9 ], [ 10 ], [ 11 ], [ 1 ], [ 2 ], [ 3, 6 ], [ 12, 15 ], [ 13, 16 ], [ 14, 17 ], [ 4, 7 ], [ 5, 8 ] ] ]
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95-->89:[ ( 2, 4, 9,18,17,11, 6,13,10)( 5,15,14,16, 7, 8,12), [ [ 9 ], [ 2 ], [ 1 ], [ 11 ], [ 10 ], [ 6, 15 ], [ 3, 12 ], [ 7, 16 ], [ 5, 14 ], [ 4, 13 ], [ 8, 17 ] ] ]
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95-->85:[ ( 2, 3)( 4, 5, 8, 6, 7)(11,12)(14,15), [ [ 2 ], [ 1 ], [ 6 ], [ 3 ], [ 7 ], [ 5 ], [ 4 ], [ 8 ], [ 9, 10, 11 ], [ 12, 13, 14 ], [ 15, 16, 17 ] ] ]
95-->77:[ ( 2, 4, 8,12, 5,16, 9,15,13,10)( 6,11)(14,18,17), [ [ 9 ], [ 1, 2 ], [ 10, 11 ], [ 3, 6 ], [ 12, 15 ], [ 5, 7 ], [ 14, 16 ], [ 4, 8 ], [ 13, 17 ] ] ]
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Order 19: Group: No. 7. NonSchurian Scheme: No. 2.
Fusions19:=[ [ 1, [ ] ], [ 2, [ 1 ] ], [ 3, [ 1 ] ], [ 4, [ 1 ] ], [ 5, [ 3, 4 ] ], [ 6, [ 4 ] ], [ 7, [ 5, 6 ] ] ];

Explicit Fusions:
5-->4:[ [ [ 1, 2 ], [ 3, 4 ], [ 5, 6 ] ], ( 2, 5, 7, 4)( 8,13,11, 9)(10,12)(14,15,19,18,16,17) ]
5-->3:[ [ [ 1, 4, 5 ], [ 2, 3, 6 ] ], ( 2,19,13,14,12, 3, 7, 5,17, 4, 8,18)( 6,10, 9)(11,16) ]
6-->4:[ [ [ 1, 7, 8 ], [ 2, 3, 5 ], [ 4, 6, 9 ] ], ( 2,15, 6,16, 4)( 3,17, 7,14,10,12, 9,13,18, 5)(11,19) ]
7-->6:[ ( 2, 3, 5, 9,17, 6,11,18, 4, 7,13,14,12,16, 8,15,10,19), [ [ 1, 18 ], [ 2, 17 ], [ 3, 16 ], [ 4, 15 ], [ 5, 14 ], [ 6, 13 ], [ 7, 12 ], [ 8, 11 ], [ 9, 10 ] ] ]
7-->5:[ ( 2, 7, 8, 5,10, 9, 3,16,13, 4,14,12, 6,18,17,19), [ [ 8, 12, 18 ], [ 1, 7, 11 ], [ 4, 6, 9 ], [ 10, 13, 15 ], [ 2, 3, 14 ], [ 5, 16, 17 ] ] ]

Order 20: Groups: Nos. 91 to 95.
Fusions20:=[[1,[]],[2,[1]],[3,[1]],[4,[1]],[5,[1]],[6,[2,3]],[7,[2 ] ],[ 8, [ 2, 5 ] ],[ 9, [ 2, 5 ] ],[ 10, [ 2 ] ],[ 11, [ 4 ] ],[ 12, [ 3, 4 ] ],[ 13, [ 5 ] ],[ 14, [3 ] ],[ 15, [ 4, 5 ] ],[ 16, [ 6 ] ],[ 17, [ 6 ] ],[ 18, [ 6, 14 ] ],[ 19, [ 6, 8 ] ],[ 20, [ 8 ] ],[ 21, [ 15 ] ],[ 22, [ 7 ] ],[ 23, [ 11, 15 ] ],[ 24, [ 15 ] ],[ 25, [15 ] ],[ 26, [ 11 ] ],[ 27, [ 16, 18 ] ],[ 28, [ 9, 16, 19 ] ],[ 29, [ 17, 18 ] ],[ 30, [ 17, 19 ] ],[ 31, [ 18 ] ],[ 32, [ 12, 19, 21 ] ],[ 33, [ 18 ] ],[ 34, [ 7, 9, 10, 13 ] ],[ 35, [ 22 ] ],[ 36, [ 8, 9, 21, 24 ] ],[ 37, [ 8, 21, 25 ] ],[ 38, [ 11, 12, 14 ] ],[ 39, [23, 24 ] ],[ 40, [ 23, 25 ] ], [ 41, [ 14 ] ],[ 42, [ 23, 26 ] ],[ 43, [ 20,21, 23 ] ],[ 44, [ 8, 13, 21, 23 ] ],[ 45, [ 20 ] ],[ 46, [ 18, 19, 20 ] ],[ 47, [ 21, 32 ] ],[ 48, [ 7, 19, 20 ] ],[ 49, [ 32 ] ],[ 50, [ 18, 41 ] ],[ 51, [ 3, 22 ] ],[ 52, [ 39, 42 ] ],[ 53, [ 40, 42 ] ],[ 54, [ 27, 28, 46 ] ],[ 55, [ 28, 32, 36 ] ],[ 56, [ 28, 48 ] ],[ 57, [ 27, 50 ] ],[ 58, [ 29, 30, 46 ] ],[ 59, [ 30, 48 ] ],[ 60, [ 30, 32, 37 ] ], [ 61, [ 29, 50 ] ],[ 62, [ 36, 39, 43 ] ],[ 63, [ 37, 40, 43 ] ],[ 64, [ 36, 39, 44 ] ],[ 65, [ 37, 40, 44 ] ],[ 66, [ 35, 51 ] ],[ 67, [ 32, 38, 43, 46 ] ],[ 68, [ 32, 43, 48 ] ],[ 69, [ 26, 38, 41 ] ], [ 70, [ 31, 33, 57 ] ],[ 71, [ 42, 43 ] ],[ 72, [ 42, 43, 45 ] ],[ 73, [ 67 ] ],[ 74, [ 45, 46 ] ][ 75, [ 67 ] ][ 76, [ 45, 46, 50 ] ],[ 77, [ 52, 62, 71 ] ],[ 78, [ 53, 63, 71 ] ],[ 79, [ 52, 62, 72 ] ],[ 80, [ 53, 63, 72] ], [ 81, [ 47, 54, 55, 62, 67 ] ],[ 82, [ 54, 74 ] ],[ 83, [ 34, 49, 55, 56, 62, 64, 68 ] ],[ 84, [ 54, 57, 76 ] ],[ 85, [ 58, 74 ] ],[ 86, [ 49, 58, 60, 63, 67 ] ],[ 87, [ 22, 47, 59, 60, 63, 68 ] ],[ 88, [ 58, 61, 76 ] ], [ 89, [ 67, 72, 74 ] ],[ 90, [ 67, 69, 72, 76 ] ],[ 91, [ 33, 75, 80, 85, 86, 89 ] ],[ 92, [ 73, 80, 86, 88, 90 ] ], [ 93, [ 51, 53, 78, 87 ] ],[ 94, [ 73, 77, 79, 81, 82, 89 ] ], [ 95, [ 79, 81, 84, 90 ] ] ];

Explicit Fusions: 6-->3:[ [ [ 1, 2 ], [ 3 ] ], () ]
6-->2:[ [ [ 1 ], [ 2, 3 ] ], () ]
7-->2:[ [ [ 1 ], [ 2, 3 ] ], () ]
8-->5:[ [ [ 1, 2 ], [ 3 ] ], () ]
8-->2:[ [ [ 1 ], [ 2, 3 ] ], () ]
9-->5:[ ( 2, 3, 4, 5, 6, 7, 8, 9,10,11), [ [ 2 ], [ 1, 3 ] ] ]
9-->2:[ [ [ 1 ], [ 2, 3 ] ], ( 4,12,16,18,19,11, 7, 5)( 6,13, 8,14,17,10,15, 9) ]
10-->2:[ [ [ 1 ], [ 2, 3 ] ], ( 4,12,19,11, 7, 5)( 6,17,10,18,14,16,15, 9)( 8,20,13) ]
11-->4:[ [ [ 1, 2 ], [ 3 ] ], () ]
12-->4:[ ( 2, 5, 8,10,12,13,14,15,16, 4, 7, 9,11, 3, 6), [ [ 2 ], [ 1, 3 ] ] ]
12-->3:[ [ [ 1 ], [ 2, 3 ] ], ( 6, 9)( 7,13)( 8,17)(11,14)(12,18)(16,19) ]
13-->5:[ [ [ 1, 2 ], [ 3 ] ], () ]
14-->3:[ [ [ 1 ], [ 2, 3 ] ], () ]
15-->5:[ [ [ 1, 2 ], [ 3 ] ], () ]
15-->4:[ [ [ 1 ], [ 2, 3 ] ], () ]
16-->6:[ ( 2, 3)( 6, 7)(10,11)(14,15)(18,19), [ [ 2 ], [ 1, 3 ], [ 4 ] ] ]
17-->6:[ [ [ 1 ], [ 2, 3 ], [ 4 ] ], () ]
18-->14:[ [ [ 1, 2 ], [ 3 ], [ 4 ] ], () ]
18-->6:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], () ]
19-->8:[ ( 3, 5, 7, 9,11)( 4, 6, 8,10,12), [ [ 1 ], [ 3 ], [ 2, 4 ] ] ]
19-->6:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], ( 7,13, 9)( 8,14,10)(11,15,17)(12,16,18) ]
20-->8:[ [ [ 1 ], [ 2, 3 ], [ 4 ] ], () ]
21-->15:[ ( 2, 3, 4, 5, 6)(12,13,14,15,16), [ [ 2 ], [ 1, 3 ], [ 4 ] ] ]
21-->8:[ [ [ 1 ], [ 2, 3 ], [ 4 ] ], ( 4, 7, 5)( 6, 8, 9)(14,17,15)(16,18,19) ]
22-->7:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], ( 3, 5, 6, 8, 4, 7)( 9,11,13,12,17)(10,19)(14,20,15)(16,18) ]
23-->15:[ [ [ 1, 2 ], [ 3 ], [ 4 ] ], () ]
23-->11:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], () ]
24-->15:[ ( 6,11)( 7,12)( 8,13)( 9,14)(10,15), [ [ 1 ], [ 3 ], [ 2, 4 ] ] ]
25-->15:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], () ]
26-->11:[ [ [ 1, 2 ], [ 3, 4 ], [ 5 ] ], ( 4, 5)( 9,10)(14,15)(19,20) ]
27-->18:[ ( 2, 3)( 6, 7)(10,11)(14,15)(18,19), [ [ 2 ], [ 1, 3 ], [ 4 ], [ 5 ] ] ]
27-->16:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], () ]
28-->19:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ] ], () ]
28-->16:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], ( 7,13, 9)( 8,14,10)(11,15,17)(12,16,18) ]
28-->9:[ ( 2, 4, 5, 6, 7, 8, 9,10,11,12, 3)(13,14)(15,16)(17,18)(19,20), [ [ 3 ], [ 1, 4 ], [ 2, 5 ] ] ]
29-->18:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ] ], () ]
29-->17:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], () ]
30-->19:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ] ], () ]
30-->17:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], ( 7,13, 9)( 8,14,10)(11,15,17)(12,16,18) ]
31-->18:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5 ] ], ( 6,11, 8,12,10, 9, 7)(14,15)(18,20,19) ]
32-->21:[ ( 3, 5, 7, 9,11)( 4, 6, 8,10,12), [ [ 1 ], [ 3 ], [ 4 ], [ 2, 5 ] ] ]
32-->19:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5 ] ], ( 6, 9, 7)( 8,10,11)(14,17,15)(16,18,19) ]
32-->12:[ [ [ 1, 2 ], [ 3 ], [ 4, 5 ] ], () ]
33-->18:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5 ] ], ( 6,11, 8,12,10, 9, 7)(14,15)(18,20,19) ]
34-->13:[ ( 2, 3, 4, 5, 9,13, 7,11)( 6,10,14, 8,12), [ [ 2 ], [ 4 ], [ 1, 3, 5 ] ] ]
34-->10:[ [ [ 1 ], [ 2, 5 ], [ 3, 4 ] ], ( 3,16, 9,17, 8,15,11)( 4, 5,18, 7,20,12,10,19,14,13, 6) ]
34-->9:[ [ [ 1 ], [ 2, 4 ], [ 3, 5 ] ], ( 6, 9,12)( 7,10,13)( 8,11,14) ]
34-->7:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ] ], ( 4, 6, 7, 5)(10,15,12,16,18,19,14,17,13,11) ]
35-->22:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ] ], ( 4, 6, 5) ]
36-->24:[ ( 2, 3, 4, 5, 6), [ [ 2 ], [ 1, 3 ], [ 4 ], [ 5 ] ] ]
36-->21:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], (12,16,15,14,13) ]
36-->9:[ [ [ 1 ], [ 2, 5 ], [ 3, 4 ] ], ( 3,18,11)( 4,17,10,20, 7, 5)( 6,19,15,14, 8)( 9,16)(12,13) ]
37-->25:[ ( 2, 3, 4, 5, 6), [ [ 2 ], [ 1, 3 ], [ 4 ], [ 5 ] ] ]
37-->21:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], (12,16,15,14,13) ]
38-->14:[ ( 2, 6, 9, 3, 7,10,12,14,15,16,17, 5)( 4, 8,11,13), [ [ 3 ], [ 1, 4 ], [ 2, 5 ] ] ]
38-->12:[ ( 2, 6, 3, 7, 4, 8, 5)(10,12,18,14,13)(11,15,16,19,17), [ [ 3 ], [ 1, 2 ], [ 4, 5 ] ] ]
38-->11:[ [ [ 1 ], [ 2 ], [ 3, 4, 5 ] ], ( 7, 9,15,19,17,11)( 8,12,10,18,14,16) ]
39-->24:[ [ [ 1, 2 ], [ 3 ], [ 4 ], [ 5 ] ], () ]
39-->23:[ ( 6,11)( 7,12)( 8,13)( 9,14)(10,15), [ [ 1 ], [ 2 ], [ 4 ], [ 3, 5 ] ] ]
40-->25:[ [ [ 1, 2 ], [ 3 ], [ 4 ], [ 5 ] ], () ]
40-->23:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], () ]
41-->14:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ] ], (13,17)(14,18)(15,19)(16,20) ]
42-->26:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5, 6 ] ], () ]
42-->23:[ [ [ 1, 2 ], [ 3, 4 ], [ 5 ], [ 6 ] ], ( 4, 5)( 9,10)(12,13)(17,18) ]
43-->23:[ ( 2, 3, 4, 7, 5, 8, 6)(12,13,14,17,15,18,16), [ [ 2 ], [ 4 ], [ 1, 3, 5 ], [ 6 ] ] ]
43-->21:[ [ [ 1 ], [ 2, 4 ], [ 3, 5 ], [ 6 ] ], ( 5, 7)( 6, 8)(15,17)(16,18) ]
43-->20:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ], [ 6 ] ], ( 4, 5)( 8, 9)(14,15)(18,19) ]
44-->23:[ ( 2, 3, 4, 5, 6)(12,13,14,15,16), [ [ 2 ], [ 3 ], [ 1, 4, 5 ], [ 6 ] ] ]
44-->21:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ], [ 6 ] ], ( 7, 9, 8,10)(17,19,18,20) ]
44-->13:[ [ [ 1, 3 ], [ 2, 4, 5 ], [ 6 ] ], ( 2, 6, 7, 4)( 3, 5)(12,16,17,14)(13,15) ]
45-->20:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ], [ 6 ] ], ( 7, 9)( 8,10)(17,19)(18,20) ]
46-->20:[ ( 3, 5, 7,13, 9,15,11)( 4, 6, 8,14,10,16,12), [ [ 1 ], [ 3 ], [ 5 ], [ 2, 4, 6 ] ] ]
46-->19:[ [ [ 1 ], [ 2 ], [ 3, 5 ], [ 4, 6 ] ], ( 9,13)(10,14)(11,15)(12,16) ]
46-->18:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5, 6 ] ], ( 7, 9)( 8,10)(15,17)(16,18) ]
47-->32:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5, 6 ] ], ( 3, 4)( 5, 7, 8)(10,12,11)(13,16,19,18,14,20) ]
48-->20:[ ( 3, 5, 7, 9,11)( 4, 6, 8,10,12), [ [ 1 ], [ 3 ], [ 4 ], [ 2, 5, 6 ] ] ]
48-->19:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5, 6 ] ], (13,17,15,19)(14,18,16,20) ]
48-->7:[ [ [ 1 ], [ 2, 4 ], [ 3, 5, 6 ] ], ( 3, 9, 7)( 4,10, 8)( 5,11,15,13)( 6,12,16,14)(17,19)(18,20) ]
49-->32:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5, 6 ] ], ( 3, 4)( 5, 6, 8, 7)( 9,12)(13,16,20)(14,19,17,18) ]
50-->41:[ [ [ 1, 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ] ], () ]
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51-->22:[ ( 3,15, 8,20)( 4,17)( 5,18, 6,19, 7,16)( 9,14)(10,11), [ [ 1 ], [ 6 ], [ 4, 5 ], [ 2, 3 ] ] ]
51-->3:[ ( 2, 3, 4, 5)( 6, 9)( 7,10,12,18,14,13)( 8,11,17)(16,20,19), [ [ 2 ], [ 1, 3, 4, 5, 6 ] ] ]
52-->42:[ ( 6,11)( 7,12)( 8,13)( 9,14)(10,15), [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 6 ], [ 5, 7 ] ] ]
52-->39:[ [ [ 1, 2 ], [ 3, 4 ], [ 5 ], [ 6 ], [ 7 ] ], ( 4, 5)( 9,10)(12,13)(19,20) ]
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53-->40:[ [ [ 1, 2 ], [ 3, 4 ], [ 5 ], [ 6 ], [ 7 ] ], ( 4, 5)( 9,10)(12,13)(17,18) ]
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55-->32:[ ( 2, 3)( 9,13)(10,14)(11,15)(12,16), [ [ 2 ], [ 1, 3 ], [ 4 ], [ 6 ], [ 5, 7 ] ] ]
55-->28:[ ( 2, 4)( 5,19,13,11)( 6, 7,20, 9)(10,18)(12,17,14,15), [ [ 3 ], [ 2 ], [ 1 ], [ 4, 7 ], [ 5, 6 ] ] ]
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58-->29:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ], [ 6, 7 ] ], ( 7, 9)( 8,10)(15,17)(16,18) ]
59-->48:[ [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ] ], () ]
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62-->36:[ [ [ 1 ], [ 2, 4 ], [ 3, 5 ], [ 6 ], [ 7 ] ], ( 5, 7)( 6, 8) ]
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65-->40:[ ( 2, 3, 4, 5, 6), [ [ 2 ], [ 3 ], [ 1, 4, 5 ], [ 6 ], [ 7 ] ] ]
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Order 21: Groups: No. 31, 32.
Fusions21:=[ [ 1, [ ] ], [ 2, [ 1 ] ], [ 3, [ 1 ] ], [ 4, [ 1 ] ], [ 5, [ 2 ] ], [ 6, [ 2, 3 ] ], [ 7, [ 2 ] ], [ 8, [ 3 ] ], [ 9, [ 1 ] ], [ 10, [ 3 ] ], [ 11, [ 5, 7 ] ], [ 12, [ 3 ] ], [ 13, [ 2 ] ], [ 14, [ 6 ] ], [ 15, [ 8, 10 ] ], [ 16, [ 5, 13 ] ], [ 17, [ 5, 6, 10 ] ], [ 18, [ 10, 12 ] ], [ 19, [ 2, 4, 9 ] ], [ 20, [ 6, 7, 8 ] ], [ 21, [ 8, 12 ] ], [ 22, [ 6, 12, 13 ] ], [ 23, [ 7, 13 ] ], [ 24, [ 15, 18, 21 ] ], [ 25, [ 11, 16, 23 ] ], [ 26, [ 11, 14, 15, 17, 20 ] ], [ 27, [ 14, 22 ] ], [ 28, [ 16, 17, 18, 22 ] ], [ 29, [ 4, 9, 17, 18 ] ], [ 30, [ 20, 21, 22, 23 ] ], [ 31, [ 19, 24, 26, 29 ] ], [ 32, [ 24, 25, 26, 27, 28, 30 ] ] ];

Explicit Fusions: 5-->2:[ [ [ 1, 2 ], [ 3 ] ], () ]
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18-->10:[ [ [ 1, 2, 3 ], [ 4 ], [ 5 ] ], () ]
19-->9:[ [ [ 1, 2 ], [ 3, 4 ], [ 5 ] ], () ]
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21-->8:[ [ [ 1, 4, 5 ], [ 2, 3, 6 ], [ 7 ] ], ( 2, 3, 4, 7)( 5, 6)( 9,10,11,14)(12,13)(16,17,18,21)(19,20) ]
22-->13:[ [ [ 1 ], [ 2, 5 ], [ 3, 6 ], [ 4, 7 ] ], ( 5,10, 6,12,16, 8,11,14,15,17,18,20,19, 9,13, 7) ]
22-->12:[ [ [ 1, 5, 6, 7 ], [ 2 ], [ 3 ], [ 4 ] ], ( 2, 4, 6, 8)( 3, 5, 7, 9,10,11,14,19,17,13,18,16,12,15) ]
22-->6:[ [ [ 1 ], [ 2, 3, 4 ], [ 5, 6, 7 ] ], (12,14,18,16)(13,15,19,17) ]
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26-->14:[ [ [ 1, 2 ], [ 3, 4 ], [ 5, 6 ], [ 7, 8 ] ], ( 2, 3)( 4, 7, 6, 9)( 5, 8)(10,12)(13,15,14)(20,21) ]
26-->11:[ [ [ 1 ], [ 2 ], [ 3, 5, 8 ], [ 4, 6, 7 ] ], ( 2, 3)( 4,18, 5,13, 6, 9,14,12,15,20,19,10, 7, 8,17,21)(11,16) ]
27-->22:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5 ], [ 6, 7 ], [ 8 ], [ 9, 10 ] ], ( 4,16, 9,11,18,14, 6, 5,17, 7)( 8,10,20,13,21,15)(12,19) ]
27-->14:[ [ [ 1 ], [ 2, 5, 8 ], [ 3, 6, 10 ], [ 4, 7, 9 ] ], ( 2, 3)( 4,16,19, 8,10,21,18, 9)( 5,11,13,20,14, 6)( 7,17,15,12) ]
28-->22:[ [ [ 1, 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6, 7 ], [ 8, 9 ], [ 10, 11 ] ], ( 4, 8, 6, 5, 9, 7)(10,20,14,13,19,17)(11,21,15,12,18,16) ]
28-->18:[ ( 2,15,13,19, 9)( 3, 8)( 6, 7)(10,11,12,18)(16,21)(17,20), [ [ 5 ], [ 3 ], [ 4 ], [ 2, 6, 8, 10 ], [ 1, 7, 9, 11 ] ] ]
28-->17:[ ( 4, 9, 7, 5, 8)(10,15,11,14,12,21,19,13,20,16,18), [ [ 1 ], [ 2 ], [ 3, 4, 5 ], [ 6, 8, 10 ], [ 7, 9, 11 ] ] ]
28-->16:[ ( 2, 3)( 4,11,13,14,21, 5,15,16,19)( 6,20, 8, 9)( 7,18)(10,12), [ [ 2 ], [ 1 ], [ 5, 10, 11 ], [ 3, 6, 7 ], [ 4, 8, 9 ] ] ]
29-->18:[ ( 2, 8)( 3,20,13,10,19,21,14,15,17,12, 9)( 4, 5)(11,16), [ [ 5 ], [ 3 ], [ 4 ], [ 1, 7, 9, 11 ], [ 2, 6, 8, 10 ] ] ]
29-->17:[ ( 4, 7, 6, 9, 5, 8)(10,11)(12,19,15,14,13,20,16,21,17,18), [ [ 1 ], [ 2 ], [ 3, 4, 5 ], [ 6, 8, 10 ], [ 7, 9, 11 ] ] ]
29-->9:[ [ [ 1, 2, 3, 6, 7 ], [ 4, 5, 10, 11 ], [ 8, 9 ] ], ( 2,15,10,19,12,21,11, 8, 9,18,13, 6,20, 5,14, 4,17)( 3,16) ]
29-->4:[ [ [ 1, 2, 3, 4, 10, 11 ], [ 5, 6, 7, 8, 9 ] ], ( 2,15, 7,14, 6,10,11,13,20, 4,16, 3, 8,17, 5,12,21)(18,19) ]
30-->23:[ ( 2, 4,10, 8)( 3, 7,19,18,17,15,12, 5,13, 6,16,14,11, 9), [ [ 7 ], [ 1, 9 ], [ 2, 8 ], [ 3, 10 ], [ 4, 11 ], [ 5, 12 ], [ 6, 13 ] ] ]
30-->22:[ ( 2, 5, 7, 9, 3, 4, 6, 8)(11,12)(15,16)(19,20), [ [ 7 ], [ 1, 2 ], [ 3, 4 ], [ 5, 6 ], [ 8, 9 ], [ 10, 11 ], [ 12, 13 ] ] ]
30-->21:[ ( 9,19,17,20,14,11,16,12)(13,21,18), [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7, 8, 9, 10, 11, 12, 13 ] ] ]
30-->20:[ ( 2, 9, 3, 4, 5, 8)( 6, 7)(11,13,21,15,14)(12,18,16,17,20), [ [ 7 ], [ 2, 3, 6 ], [ 1, 4, 5 ], [ 8, 10, 13 ], [ 9, 11, 12 ] ] ]
31-->29:[ ( 2, 4, 8, 3, 6, 7, 5, 9,10,14,11,18,13,15)(12,19)(17,21), [ [ 14 ], [ 7 ], [ 1, 6 ], [ 2, 5 ], [ 3, 4 ], [ 8, 13 ], [ 17, 18 ], [ 9, 12 ], [ 15, 20 ], [ 10, 11 ], [ 16, 19 ] ] ]
31-->26:[ ( 2, 4, 7, 9,20,16,11,14,15, 3, 5, 6, 8)(10,19)(12,21,17), [ [ 7 ], [ 14 ], [ 1, 2, 4 ], [ 3, 5, 6 ], [ 15, 16, 18 ], [ 10, 12, 13 ], [ 17, 19, 20 ], [ 8, 9, 11 ] ] ]
31-->24:[ ( 3, 5, 6, 4, 7)( 8,18,14,20,11,16, 9,17,12,19,13,21,10,15), [ [ 1 ], [ 6 ], [ 5 ], [ 2 ], [ 4 ], [ 3 ], [ 14, 15, 16, 17, 18, 19, 20 ], [ 7, 8, 9, 10, 11, 12, 13 ] ] ]
31-->19:[ ( 2, 9, 5,12,17,13,11, 8)( 3,15)( 4, 6,21,18)( 7,10,20,16), [ [ 7, 14 ], [ 8, 17 ], [ 1, 3, 10, 15 ], [ 4, 6, 12, 16 ], [ 2, 5, 9, 11, 13, 18, 19, 20 ] ] ]
32-->30:[ ( 2, 3, 4, 6, 5, 7)( 9,10,14,12,20,17,15)(11,18,19,21,13,16), [ [ 6 ], [ 1 ], [ 2 ], [ 5 ], [ 3 ], [ 4 ], [ 7, 14 ], [ 8, 15 ], [ 13, 20 ], [ 9, 16 ], [ 12, 19 ], [ 10, 17 ], [ 11, 18 ] ] ]
32-->28:[ ( 2, 5, 8, 3, 7, 4, 9,11,19,20,16,13,14,10,15)(12,18,21), [ [ 14 ], [ 7 ], [ 1, 6 ], [ 2, 5 ], [ 3, 4 ], [ 8, 13 ], [ 15, 20 ], [ 9, 12 ], [ 16, 19 ], [ 10, 11 ], [ 17, 18 ] ] ]
32-->27:[ ( 2, 5,16, 6,10,15)( 3,11,21, 8)( 4,17,12,19,20,14, 7), [ [ 7, 14 ], [ 1, 6 ], [ 13, 15 ], [ 8, 20 ], [ 2, 5 ], [ 12, 16 ], [ 9, 19 ], [ 3, 4 ], [ 11, 17 ], [ 10, 18 ] ] ]
32-->26:[ ( 2, 9,18,20,21,19,15)( 3, 8)( 4, 6, 5, 7)(10,17,14)(11,12,16,13), [ [ 14 ], [ 7 ], [ 3, 5, 6 ], [ 1, 2, 4 ], [ 10, 12, 13 ], [ 15, 16, 18 ], [ 8, 9, 11 ], [ 17, 19, 20 ] ] ]
32-->25:[ ( 2, 8, 3,10,12,20,14, 6,13,15)( 4,17,11,16, 9, 7)( 5,21), [ [ 14 ], [ 7 ], [ 6, 13, 20 ], [ 1, 8, 15 ], [ 2, 9, 16 ], [ 5, 12, 19 ], [ 3, 10, 17 ], [ 4, 11, 18 ] ] ]
32-->24:[ ( 2, 3, 4, 6, 5, 7)( 8,14,13,11)( 9,12,10)(16,17,18,20,19,21), [ [ 6 ], [ 1 ], [ 2 ], [ 5 ], [ 3 ], [ 4 ], [ 7, 8, 9, 10, 11, 12, 13 ], [ 14, 15, 16, 17, 18, 19, 20 ] ] ]

Order 22: Groups: No. 15, 16.
Fusions22:=[ [ 1, [ ] ], [ 2, [ 1 ] ], [ 3, [ 1 ] ], [ 4, [ 2, 3 ] ], [ 5, [ 2 ] ], [ 6, [ 3 ] ], [ 7, [ 3 ] ], [ 8, [ 4, 6, 7 ] ], [ 9, [ 4, 5, 6 ] ], [ 10, [ 2 ] ], [ 11, [ 3 ] ], [ 12, [ 6, 11 ] ], [ 13, [ 4, 10, 11 ] ], [ 14, [ 5, 10 ] ], [ 15, [ 8, 12, 13 ] ], [ 16, [ 9, 12, 13, 14 ] ] ];

Explicit Fusions: 4-->3:[ [ [ 1, 3 ], [ 2 ] ], ( 2, 3, 4, 5, 6, 7, 8, 9,10,11,12) ]
4-->2:[ [ [ 1 ], [ 2, 3 ] ], ( 4,13, 8,15, 9, 6,14,18,20,21,12,17,10,16,19,11, 7, 5) ]
5-->2:[ [ [ 1 ], [ 2, 3 ] ], () ]
6-->3:[ [ [ 1, 2 ], [ 3 ] ], () ]
7-->3:[ [ [ 1, 2 ], [ 3 ] ], ( 2,13, 3,14, 4,15, 5,16, 6,17, 7,18, 8,19, 9,20,10,21,11,22,12) ]
8-->7:[ [ [ 1, 2 ], [ 3 ], [ 4, 5 ] ], ( 2,12, 6,11, 7, 4, 9)( 3, 8)( 5,10)(13,22,20,21,17,19,15,16,18) ]
8-->6:[ [ [ 1, 2, 3 ], [ 4 ], [ 5 ] ], ( 2,21, 7,14, 3,22,11,15,12, 9,17,10,16, 6,18)( 4,20, 8,13, 5,19) ]
8-->4:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ] ], ( 3,15, 4,17, 9,19, 7,16,12,18, 6,13,10,22)( 5,21,11,14, 8,20) ]
9-->6:[ [ [ 1, 4, 5 ], [ 2 ], [ 3 ] ], ( 2, 3, 4, 5, 6, 7, 8, 9,10,11,12) ]
9-->5:[ [ [ 1 ], [ 2, 4 ], [ 3, 5 ] ], ( 4,13, 8,15, 9, 6,14,18,20,21,12,17,10,16,19,11, 7, 5) ]
9-->4:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ] ], () ]
10-->2:[ [ [ 1 ], [ 2, 3, 4, 5, 6 ] ], () ]
11-->3:[ [ [ 1, 2, 3, 4, 5 ], [ 6 ] ], () ]
12-->11:[ ( 2, 8,11, 5, 7)( 3, 9,10, 4, 6)(13,19,22,16,18)(14,20,21,15,17), [ [ 5, 6 ], [ 9, 10 ], [ 3, 4 ], [ 1, 2 ], [ 7, 8 ], [ 11 ] ] ]
12-->6:[ [ [ 1, 3, 6, 8, 10 ], [ 2, 4, 5, 7, 9 ], [ 11 ] ], ( 2, 5, 8, 4, 3, 6,10,11, 7, 9)(13,16,19,15,14,17,21,22,18,20) ]
13-->11:[ ( 2,22,12, 7, 4, 3)( 5,21,13,17,15, 8)( 6,20,11)( 9,19,10,18,14,16), [ [ 2 ], [ 4 ], [ 6 ], [ 8 ], [ 10 ], [ 1, 3, 5, 7, 9, 11 ] ] ]
13-->10:[ ( 3, 8,18,12,20, 4, 9,15,13,22)( 5, 7,16,11,21)( 6,10,17,14,19), [ [ 1 ], [ 10, 11 ], [ 2, 3 ], [ 8, 9 ], [ 4, 5 ], [ 6, 7 ] ] ]
13-->4:[ [ [ 1 ], [ 2, 4, 6, 8, 10 ], [ 3, 5, 7, 9, 11 ] ], ( 5, 7,11,19,17,13)( 6, 8,12,20,18,14)( 9,15)(10,16) ]
14-->10:[ ( 3, 5)( 4, 6), [ [ 1 ], [ 2, 3 ], [ 4, 5 ], [ 6, 7 ], [ 8, 9 ], [ 10, 11 ] ] ]
14-->5:[ [ [ 1 ], [ 2, 4, 7, 9, 11 ], [ 3, 5, 6, 8, 10 ] ], ( 3,19,17,13)( 4,20,18,14)( 5, 9)( 6,10)( 7,11,15,21)( 8,12,16,22) ]
15-->13:[ ( 2, 3, 7,20,13, 6,19,17,22, 5,15,14,10, 8,16,18,21, 9,12)( 4,11), [ [ 11 ], [ 1, 10 ], [ 12, 21 ], [ 2, 9 ], [ 13, 20 ], [ 3, 8 ], [ 14, 19 ], [ 4, 7 ], [ 15, 18 ], [ 5, 6 ], [ 16, 17 ] ] ]
15-->12:[ ( 3, 5, 9, 6,11)( 4, 7,10)(14,16,20,17,22)(15,18,21), [ [ 1 ], [ 10 ], [ 9 ], [ 2 ], [ 8 ], [ 3 ], [ 7 ], [ 4 ], [ 6 ], [ 5 ], [ 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 ] ] ]
15-->8:[ ( 2,13, 4,16, 5,15, 3,19,10,14,11,21, 7,20, 9,18, 8,22,12)( 6,17), [ [ 11 ], [ 12, 14, 15, 16, 20 ], [ 13, 17, 18, 19, 21 ], [ 1, 3, 4, 5, 9 ], [ 2, 6, 7, 8, 10 ] ] ]
16-->14:[ ( 2, 6,20,14, 8,18,22, 4,12)( 3, 7,21, 9,13, 5,15,11)(17,19), [ [ 11 ], [ 10, 21 ], [ 1, 12 ], [ 2, 13 ], [ 9, 20 ], [ 3, 14 ], [ 8, 19 ], [ 4, 15 ], [ 7, 18 ], [ 5, 16 ], [ 6, 17 ] ] ]
16-->13:[ ( 2, 4,12)( 3, 8,15,14,10, 7,19,17,22, 5,16,18,21, 9,11)( 6,20,13), [ [ 11 ], [ 1, 10 ], [ 12, 21 ], [ 2, 9 ], [ 13, 20 ], [ 3, 8 ], [ 14, 19 ], [ 4, 7 ], [ 15, 18 ], [ 5, 6 ], [ 16, 17 ] ] ]
16-->12:[ ( 2, 3, 4, 6,10, 5, 8, 9, 7,11)(13,14,15,17,21,16,19,20,18,22), [ [ 10 ], [ 1 ], [ 2 ], [ 9 ], [ 3 ], [ 8 ], [ 4 ], [ 7 ], [ 5 ], [ 6 ], [ 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 ] ] ]
16-->9:[ ( 2, 9, 7, 5,12)( 3, 6,10, 8, 4,11)(13,19,14,16,22)(15,21,18)(17,20), [ [ 11 ], [ 2, 6, 7, 8, 10 ], [ 1, 3, 4, 5, 9 ], [ 13, 17, 18, 19, 21 ], [ 12, 14, 15, 16, 20 ] ] ]

Order 23: Group: No. 22. NonSchurian Schemes: Nos. 2 to 19.
Fusions23:=[ [ 1, [ ] ], [ 2, [ 1 ] ], [ 3, [ 1 ] ], [ 4, [ 1 ] ], [ 5, [ 1 ] ], [ 6, [ 1 ] ], [ 7, [ 1 ] ], [ 8, [ 1 ] ], [ 9, [ 1 ] ], [ 10, [ 1 ] ], [ 11, [ 1 ] ], [ 12, [ 1 ] ], [ 13, [ 1 ] ], [ 14, [ 1 ] ], [ 15, [ 1 ] ], [ 16, [ 1 ] ], [ 17, [ 1 ] ], [ 18, [ 1 ] ], [ 19, [ 1 ] ], [ 20, [ 1 ] ], [ 21, [ 1 ] ], [ 22, [ 20, 21 ] ] ];

Explicit Fusions:
22-->21:[ ( 2, 3, 5, 9,17,14,20, 8,15,18,12,23)( 4, 7,13,22)( 6,11,21)(10,19), [ [ 1, 22 ], [ 2, 21 ], [ 3, 20 ], [ 4, 19 ], [ 5, 18 ], [ 6, 17 ], [ 7, 16 ], [ 8, 15 ], [ 9, 14 ], [ 10, 13 ], [ 11, 12 ] ] ]
22-->20:[ ( 2,21, 7,14,13,20, 5,18,10,16,11, 6, 8,12, 9,19,15, 3,22, 4,23), [ [ 5, 7, 10, 11, 14, 15, 17, 19, 20, 21, 22 ], [ 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18 ] ] ]

Order 24: There are 750 schemes. Groups: No. 736 to 750.
See the Order 24 Fusion Table. The complete list has been worked out up to number 635, beyond that it may not be complete.

Order 25: Groups: No. 44,45.
Fusions25:= [[1,[]],[2,[1]],[3,[1]],[4,[1]],[5,[1]],[6,[1]],[7,[1]],[8,[1]],[9,[1]],[10,[1]],[11,[1]], [12,[2]],[13,[2,3]],[14,[2,3]],[15,[2,3,11]],[16,[2]],[17,[3]],[18,[3]],[19,[12,16]],[20,[13,14]],[21,[11,13]],[22,[13,15,17]],[23,[11,13,18]],[24,[11]],[25,[12]],[26,[12,13,16]],[27,[18]],[28,[17]],[29,[16]],[30,[19,25]],[31,[19,29]],[32,[24]],[33,[22,28]],[34,[21,23,27]],[35,[2]],[36,[26]],[37,[30,31]],[38,[19,22,24]],[39,[32]],[40,[25,26,29]],[41,[26,33,34,38]],[42,[19,35]],[43,[28,30,31,32,36,38,40]],[44,[37,42]],[45,[37,39,41,43]]];

Explicit Fusions: 12-->2:[ [ [ 1, 2 ], [ 3 ] ], () ]
13-->3:[ [ [ 1, 2 ], [ 3 ] ], () ]
13-->2:[ [ [ 1 ], [ 2, 3 ] ], ( 7,10,22,13,15,23,17,12,11)( 8,14,19,20,24,21, 9,18,16) ]
14-->3:[ [ [ 1, 3 ], [ 2 ] ], ( 2, 9, 6,12,20,25,16,17)( 3, 7, 8,10,23,21,18, 5,11)( 4,13,14,19,22,24) ]
14-->2:[ [ [ 1 ], [ 2, 3 ] ], ( 8,20,23,14,19,18,15,25,21,12, 9,22,13,16,10,24,17,11) ]
15-->11:[ [ [ 1, 2 ], [ 3 ] ], ( 2,12, 3,10)( 4, 6, 5, 9,13, 7,11, 8)(14,19,15,20,16,24,22,25,17,18,23,21) ]
15-->3:[ [ [ 1, 3 ], [ 2 ] ], ( 2,11,21)( 3, 8,10,24,25,18,19,15)( 4, 7, 9, 6,12)( 5,13,17,14,23,22)(16,20) ]
15-->2:[ [ [ 1 ], [ 2, 3 ] ], ( 7, 8,16,10,24,18,14,23,15,25,20,21,11)( 9,22,12)(13,17) ]
16-->2:[ [ [ 1 ], [ 2, 3 ] ], () ]
17-->3:[ [ [ 1 ], [ 2, 3 ] ], ( 2, 6, 5, 7, 3, 8, 4, 9)(10,24,23,15,20,16,17,18,12,22,25,11,14,13)(19,21) ]
18-->3:[ [ [ 1 ], [ 2, 3 ] ], ( 2, 8, 4, 6, 5, 7, 3, 9)(10,25,18,17)(11,20,16,23,15,14,22,13)(19,21) ]
19-->16:[ [ [ 1, 2 ], [ 3 ], [ 4 ] ], () ]
19-->12:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], () ]
20-->14:[ [ [ 1 ], [ 2, 3 ], [ 4 ] ], ( 3, 5, 4)( 7,10)( 8, 9,13,12)(14,19,15,16,17)(20,23,25,22,24) ]
20-->13:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], ( 2, 9, 3, 7, 5, 6, 4, 8)(10,22,24)(11,13,17)(12,15,25,20,14,18) ]
21-->13:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], ( 2, 8)( 3, 7, 5, 6, 4, 9)(10,22,24,15,25,11,13,17,21,20,14,18,12,16) ]
21-->11:[ [ [ 1, 2, 3 ], [ 4 ] ], ( 2, 9,13,10)( 3, 8, 4, 6, 5, 7,12)(14,16,24,23,22,25,18,21,17,19)(15,20) ]
22-->17:[ [ [ 1, 2 ], [ 3 ], [ 4 ] ], () ]
22-->15:[ [ [ 1, 3 ], [ 2 ], [ 4 ] ], ( 2, 6,19,17,15, 5, 9,20,12,25, 3, 7,21,16,11,24)( 4, 8,18,13,23,14)(10,22) ]
22-->13:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], ( 2, 9, 3, 7, 5, 6, 4, 8)(10,16,11,12,19,13,21,20,18,17,15,25,14,23,24) ]
23-->18:[ [ [ 1, 2 ], [ 3 ], [ 4 ] ], () ]
23-->13:[ [ [ 1 ], [ 2 ], [ 3, 4 ] ], ( 2, 7, 5, 9, 3, 8)( 4, 6)(10,24)(11,13,15,25,14,12,18,16)(17,20,19)(22,23) ]
23-->11:[ [ [ 1, 3 ], [ 2, 4 ] ], ( 2,10)( 3,17,22,18,24, 8, 4,12, 5,15, 9,16,25, 7,14, 6)(19,23) ]
24-->11:[ [ [ 1, 3 ], [ 2, 4 ] ], ( 2,19,11, 5, 6,17,23,25, 9,18,13, 4, 3,15,24,12, 7,16,20, 8,14,22,21,10) ]
25-->12:[ [ [ 1, 2 ], [ 3, 4 ], [ 5 ] ], ( 4, 5)( 9,10)(14,15)(19,20)(24,25) ]
26-->16:[ [ [ 1, 4 ], [ 2, 5 ], [ 3 ] ], ( 2, 6)( 3, 7,10,13,15,17,18,19,20,21, 5, 9,12,14,16, 4, 8,11) ]
26-->13:[ [ [ 1, 2 ], [ 3 ], [ 4, 5 ] ], () ]
26-->12:[ [ [ 1 ], [ 2 ], [ 3, 4, 5 ] ], ( 7,10,22,13,15,23,17,12,11)( 8,14,19,20,24,21, 9,18,16) ]
27-->22:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5 ] ], ( 2, 4, 3, 5)( 6, 9, 7, 8)(10,13,14,15,11,17,12)(18,23,20,24)(19,21,25) ]
27-->18:[ [ [ 1, 3 ], [ 2, 4 ], [ 5 ] ], ( 2,10,21,17,24, 9)( 3,11,25,14,20, 8, 4,13,23,15,19, 7, 5,12,22, 6)(16,18) ]
28-->17:[ [ [ 1, 3 ], [ 2, 4 ], [ 5 ] ], ( 2,13,25, 7)( 3,12,19,16,18,14,22, 8,11,21,17,24, 9,10,23, 6, 5, 4)(15,20) ]
29-->16:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ] ], (16,21)(17,22)(18,23)(19,24)(20,25) ]
30-->25:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5, 6 ] ], () ]
30-->19:[ [ [ 1, 2 ], [ 3, 4 ], [ 5 ], [ 6 ] ], ( 4, 5)( 7, 8)(14,15)(17,18)(22,23) ]
31-->29:[ [ [ 1, 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ] ], () ]
31-->19:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5, 6 ] ], (16,21)(17,22)(18,23)(19,24)(20,25) ]
32-->24:[ [ [ 1, 2 ], [ 3, 4 ], [ 5 ], [ 6 ] ], ( 2,13,25,14, 5,12,23,19, 7,10,21,15)( 3, 8,20,18, 6,11,24,16)( 4, 9,22,17) ]
33-->28:[ [ [ 1, 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ] ], ( 2,17,20, 9,25, 3,15,21, 5,14,18)( 4,16,19, 6,24, 7,22)( 8,23)(10,11,13,12) ]
33-->22:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5, 6 ] ], ( 2, 4, 3, 5)( 6, 8, 7, 9)(10,13)(11,16,12,14,15)(18,19,24,22,20,25) ]
34-->27:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5 ], [ 6 ] ], ( 2,21,12, 3,19,13, 4,18,17, 7,25,16, 8,23,15, 6,24,10)( 5,20,14, 9,22,11) ]
34-->23:[ [ [ 1, 4 ], [ 2, 3 ], [ 5 ], [ 6 ] ], ( 2,21,10)( 3,20, 6,24, 7,23,12, 4,18,13,14,16,15, 5,19, 9,25,11,17)( 8,22) ]
34-->21:[ [ [ 1, 2, 6 ], [ 3 ], [ 4 ], [ 5 ] ], ( 2,12,20, 4,11,21,23, 3,10,19,25, 6,16, 5,13,18)( 7,15,22,24)( 8,17)( 9,14) ]
35-->2:[ [ [ 1 ], [ 2, 3, 4, 5, 6 ] ], ( 7,12,10,24,18,15,25,23,16, 8,14,19,20,22,11)( 9,21)(13,17) ]
36-->26:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ], [ 6, 7 ] ], ( 2, 4, 3, 5)( 6, 7, 8, 9)(10,23)(11,18,13,22,15,25,14,21,12,19,17,20,16,24) ]
37-->31:[ [ [ 1, 2 ], [ 3, 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ] ], ( 4, 5)( 7, 8)(14,15)(17,18)(24,25) ]
37-->30:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5, 6 ], [ 7, 8 ] ], (16,21)(17,22)(18,23)(19,24)(20,25) ]
38-->28:[ [ [ 1, 3 ], [ 2, 4 ], [ 5 ], [ 6, 7 ], [ 8 ] ], ( 2, 9,22,14,13, 3, 5, 8,24,21,17,10, 6,25,19,18,20,15,11, 7,23,16,12) ]
38-->26:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5, 6 ], [ 7, 8 ] ], ( 2, 4, 3, 5)( 6, 9, 7)(10,23)(11,18,17,21,13,19,12,22,15,20,16,24,14,25) ]
38-->24:[ [ [ 1, 7 ], [ 2, 6 ], [ 3, 8 ], [ 4, 5 ] ], ( 2,17,19, 3, 5,16,18,21,13,24, 8,23,11,25,12, 7,14,20,10,22, 9, 6, 4,15) ]
38-->22:[ [ [ 1, 2 ], [ 3, 4 ], [ 5, 8 ], [ 6, 7 ] ], ( 2, 4, 3, 5)( 6, 8, 7, 9)(10,22,16,12)(11,23,17,13)(14,24)(15,25)(18,19)(20,21) ]
38-->19:[ [ [ 1 ], [ 2 ], [ 3, 5, 7 ], [ 4, 6, 8 ] ], ( 7,10,20,24,23,17,14,19,22,15,21, 9,18,16, 8,12,11) ]
39-->32:[ [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5 ], [ 6 ], [ 7, 8 ] ], ( 2, 6)( 3, 7)( 4, 5)( 8,18,10,19,12,16,13,15,11,14, 9,17)(20,23,24,25) ]
40-->29:[ [ [ 1, 7 ], [ 2, 6 ], [ 3, 8 ], [ 4, 9 ], [ 5 ] ], ( 2, 6)( 3, 7,14,12,10,17,18,19,20,21, 5, 9,16, 4, 8,15,13,11) ]
40-->26:[ [ [ 1, 2 ], [ 3, 4 ], [ 5 ], [ 6, 7 ], [ 8, 9 ] ], ( 2, 5)( 3, 4)( 6, 9, 7)(10,25,15,18,13,23,14,21,11,22,17,19)(12,24,16,20) ]
40-->25:[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5, 6, 7, 8, 9 ] ], ( 7,14,19,20,24,21, 9,18,12,15,23,13,11)( 8,10,22,17,16) ]
41-->38:[ ( 2,11, 5,24, 3,12,14,21,19,15,18,16,22, 6,10, 4,23, 7,13,17,25)( 8, 9), [ [ 12 ], [ 5 ], [ 11 ], [ 4 ], [ 1, 3 ], [ 6, 9 ], [ 7, 10 ], [ 2, 8 ] ] ]
41-->34:[ ( 2,10, 4,13,20,21,19,22, 6,14,25)( 3,12,18,23, 7,17,15,24)( 5,11), [ [ 5, 12 ], [ 4, 11 ], [ 1, 2 ], [ 3, 8 ], [ 6, 10 ], [ 7, 9 ] ] ]
41-->33:[ ( 2,10, 4,16,13,23, 7,17,11, 5,15,24, 3,12,22, 6,14,25)( 8, 9)(18,20,21,19), [ [ 5, 12 ], [ 4, 11 ], [ 1, 8 ], [ 2, 3 ], [ 9, 10 ], [ 6, 7 ] ] ]
41-->26:[ ( 2,11, 5,24, 3,14,23, 7,15,18,16,20,22, 6,10, 4,21,19,13,17,25)( 8, 9), [ [ 12 ], [ 5 ], [ 4, 11 ], [ 1, 3, 6, 9 ], [ 2, 7, 8, 10 ] ] ]
42-->35:[ ( 2, 3)( 4, 5)( 6,11,15,20,10,16,19,25)( 7,13, 9,23,17,21,12, 8,22,14,18,24), [ [ 1, 2 ], [ 6, 12 ], [ 3, 10 ], [ 5, 11 ], [ 7, 8 ], [ 4, 9 ] ] ]
42-->19:[ ( 2, 4, 3, 5)( 6,19,12,25)( 7,24,11,23,15,22,10,18)( 8,21, 9,16,13,20,14,17), [ [ 2 ], [ 1 ], [ 8, 9, 10, 11, 12 ], [ 3, 4, 5, 6, 7 ] ] ]
43-->40:[ ( 2, 3)( 4, 5)( 6, 8, 7, 9)(10,16,11,17)(14,15)(18,24,19,25)(22,23), [ [ 2 ], [ 1 ], [ 4 ], [ 3 ], [ 5, 6 ], [ 8, 10 ], [ 7, 9 ], [ 12, 14 ], [ 11, 13 ] ] ]
43-->38:[ ( 2, 3)( 6, 8, 7, 9)(10,14,11,15)(12,16,13,17)(18,22,19,23)(20,24,21,25), [ [ 1, 2 ], [ 3, 4 ], [ 6 ], [ 5 ], [ 9, 10 ], [ 7, 8 ], [ 13, 14 ], [ 11, 12 ] ] ]
43-->36:[ ( 2, 3)( 8, 9)(10,14,11,15)(18,22,19,23), [ [ 1, 2 ], [ 3, 4 ], [ 5, 6 ], [ 8, 9 ], [ 7, 10 ], [ 12, 13 ], [ 11, 14 ] ] ]
43-->32:[ ( 2, 6,20, 5, 9,19, 4,12,16,11,17,13,18)( 7,25,21)( 8,14,10,15)(22,24,23), [ [ 2, 11 ], [ 1, 12 ], [ 4, 9 ], [ 3, 10 ], [ 6, 7, 8 ], [ 5, 13, 14 ] ] ]
43-->31:[(2,14,8,4,23,22,24,17,13,15,6)(3,9,5,18,25,19,21,20,16,11,7),[[5],[6],[2,7,9],[1,8,10],[4,12,14],[3,11,13]]]
43-->30:[(2,3)(4,5)(6,18,17,8,12,19,23,10,16,11,24,13,22,14,15,7,25,9),[[2],[1],[4],[3],[6,10,14,13,9],[7,11,5,8,12]]]
43-->28:[ ( 2, 9, 7,15,10,25,22,21)( 3, 6,16,11,23,24,19, 4,17,13,18, 5,14,12,20), [ [ 11, 12 ], [ 1, 2, 6 ], [ 9, 10 ], [ 3, 4, 5 ], [ 7, 8, 13, 14 ] ] ]
44-->42:[ ( 3, 4, 5)( 7,10, 9,13,24,11,16,18,25)( 8,14,23,15,19,21)(12,20,17,22), [ [ 1, 4 ], [ 2, 3 ], [ 5, 24 ], [ 9, 20 ], [ 6, 23 ], [ 8, 21 ], [ 7, 22 ], [ 10, 19 ], [ 14, 15 ], [ 11, 18 ], [ 13, 16 ], [ 12, 17 ] ] ]
44-->37:[ ( 3, 5)( 6, 8, 7)( 9,10)(11,22,15,21,12,25)(13,24)(14,23)(16,18,17)(19,20), [ [ 1 ], [ 4 ], [ 3 ], [ 2 ], [ 5, 6, 7, 8, 9 ], [ 20, 21, 22, 23, 24 ], [ 15, 16, 17, 18, 19 ], [ 10, 11, 12, 13, 14 ] ] ]
45-->43:[ ( 2, 3, 4, 5)( 6, 7,11, 9,21)( 8,19,24,20,16)(10,13,23,18,22)(12,15,17,14,25), [ [ 4 ], [ 1 ], [ 2 ], [ 3 ], [ 5, 20 ], [ 10, 15 ], [ 6, 21 ], [ 9, 24 ], [ 11, 16 ], [ 14, 19 ], [ 7, 22 ], [ 8, 23 ], [ 12, 17 ], [ 13, 18 ] ] ] 45-->41:[ ( 2, 3, 5)( 6, 7,11,17,19,24,14,22, 9,12,21)( 8,15,18,23,13,25,10), [ [ 1, 4 ], [ 2, 3 ], [ 5, 20 ], [ 9, 21 ], [ 6, 24 ], [ 8, 22 ], [ 7, 23 ], [ 10, 15 ], [ 14, 16 ], [ 11, 19 ], [ 13, 17 ], [ 12, 18 ] ] ] 45-->39:[ ( 2, 7, 4,17,22,10,11,14,25, 5)( 3,16,18,21)( 8,13,19,15,24)( 9,23,20,12), [ [ 4, 6, 20 ], [ 1, 5, 24 ], [ 11, 21, 23 ], [ 7, 9, 19 ], [ 2, 10, 18 ], [ 3, 12, 15 ], [ 16, 17, 22 ], [ 8, 13, 14 ] ] ] 45-->37:[(2,3,4,5)(6,13,18,22,8,15,20,23,9,12,16,24,10,11,17,25,7,14,19,21),[[4],[1],[2],[3],[20,24,21,22,23],[9,8,5,6,7],[11,10,12,13,14], [18,17,19,15,16]]]

Order 26: Groups: No. 33,34.
Fusions26:= [[1,[]],[2,[1]],[3,[1]],[4,[1]],[5,[1]],[6,[1]],[7,[1]],[8,[1]],[9,[1]],[10,[1]],[11,[1]],[12,[1]],[13,[1]],[14,[2]],[15,[2,13]],[16,[13]],[17,[13]],[18,[2]],[19,[13]],[20,[14,15,17]],[21,[15,17]],[22,[14]],[23,[17]],[24,[14,18]],[25,[15,18,19]],[26,[17,19]],[27,[16,20,23]],[28,[20,22,23]],[29,[23,26]],[30,[20,24,25,26]],[31,[21,25,26]],[32,[22,24]],[33,[27,29,30]],[34,[28,29,30,32]]];

Explicit Fusions: 14-->2:[ [ [ 1 ], [ 2, 3 ] ], () ]
15-->13:[ ( 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14), [ [ 2 ], [ 1, 3 ] ] ]
15-->2:[ [ [ 1 ], [ 2, 3 ] ], ( 4,15, 9, 6,16,21,12,19,11, 7, 5)( 8,17,10,18,22,24,25,14,20,23,13) ]
16-->13:[ ( 2,15, 3,16, 4,17, 5,18, 6,19, 7,20, 8,21, 9,22,10,23,11,24,12,25,13,26,14), [ [ 3 ], [ 1, 2 ] ] ]
17-->13:[ [ [ 1, 2 ], [ 3 ] ], () ]
18-->2:[ [ [ 1 ], [ 2, 3, 4 ] ], () ]
19-->13:[ [ [ 1, 2, 3 ], [ 4 ] ], () ]
20-->17:[ ( 2, 3, 4, 5, 6, 7, 8,15, 9,16,10,17,11,18,12,19,13,20,14), [ [ 2 ], [ 4 ], [ 1, 3, 5 ] ] ]
20-->15:[ [ [ 1 ], [ 2, 4 ], [ 3, 5 ] ], ( 9,15)(10,16)(11,17)(12,18)(13,19)(14,20) ]
20-->14:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ] ], ( 4, 9, 6,10,12,13, 8,11, 7, 5)(16,21,18,22,24,25,20,23,19,17) ]
21-->17:[ ( 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14)(15,16)(17,20)(22,26,24,23), [ [ 2 ], [ 3 ], [ 1, 4, 5 ] ] ]
21-->15:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ] ], (15,21,20,22,19,23,18,24,17,26)(16,25) ]
22-->14:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ] ], ( 3,11,13, 5)( 4,12,14, 6)(15,23)(16,24)(17,19)(18,20) ]
23-->17:[ [ [ 1, 2 ], [ 3, 4 ], [ 5 ] ], ( 2, 3, 7, 6)( 4, 5)( 8, 9,13,10,12,11)(15,16,20,19)(17,18)(21,22,26,23,25,24) ]
24-->18:[ ( 3,17,13,11, 7,25)( 4,18,14,12, 8,26)( 5,23,21)( 6,24,22)( 9,15)(10,16), [ [ 1 ], [ 5, 7 ], [ 3, 4 ], [ 2, 6 ] ] ]
24-->14:[ [ [ 1 ], [ 2, 4, 5 ], [ 3, 6, 7 ] ], ( 3,15,19,21, 7,11, 5)( 4,16,20,22, 8,12, 6)( 9,13,17,25,23)(10,14,18,26,24) ]
25-->19:[ ( 2, 3, 4, 5, 6,11,20,16, 8,13,22,18,10,19,15, 7,12,21,17, 9,14), [ [ 2 ], [ 4 ], [ 6 ], [ 1, 3, 5, 7 ] ] ]
25-->18:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ], [ 6, 7 ] ], ( 4, 7, 5)( 6, 8, 9)(12,15,13)(14,16,17)(20,23,21)(22,24,25) ]
25-->15:[ [ [ 1 ], [ 2, 4, 6 ], [ 3, 5, 7 ] ], ( 7,11,19,15)( 8,12,20,16)( 9,13,21,17)(10,14,22,18) ]
26-->19:[ ( 2, 6,10,12,13, 9, 3, 4, 5, 7)( 8,11)(15,19,23,25,26,22,16,17,18,20)(21,24), [ [ 2, 3 ], [ 1, 5 ], [ 4, 6 ], [ 7 ] ] ]
26-->17:[ [ [ 1, 3, 4 ], [ 2, 5, 6 ], [ 7 ] ], ( 3, 7)( 4, 8, 5, 9,10)(11,13)(16,20)(17,21,18,22,23)(24,26) ]
27-->23:[ ( 2,17, 5,19, 7,18, 6,20, 8,22,10,23,11,24,12,26,14)( 3,16, 4,15)( 9,21)(13,25), [ [ 6 ], [ 7 ], [ 8 ], [ 9 ], [ 1, 2, 3, 4, 5 ] ] ]
27-->20:[ ( 3,21, 5,25, 7,22, 8,26)( 4,24)( 6,23)( 9,13,12,14,10)(15,19,16,17)(18,20), [ [ 1 ], [ 8, 9 ], [ 4, 5 ], [ 6, 7 ], [ 2, 3 ] ] ]
27-->16:[ [ [ 1, 5 ], [ 2, 3, 4 ], [ 6, 7, 8, 9 ] ], ( 2,13, 8, 6,11, 4)( 3,14, 7, 9, 5,12)(15,21,25,20,16,19,23,26)(22,24) ]
28-->23:[ ( 2, 3, 4, 5, 6, 7, 8,15, 9,16,10,17,11,18,12,19,13,20,14), [ [ 2 ], [ 3 ], [ 6 ], [ 7 ], [ 1, 4, 5, 8, 9 ] ] ]
28-->22:[ [ [ 1 ], [ 2, 4 ], [ 3, 5 ], [ 6, 8 ], [ 7, 9 ] ], ( 4, 9, 6,10,12,13, 8,11, 7, 5)(16,21,18,22,24,25,20,23,19,17) ]
28-->20:[ [ [ 1 ], [ 2, 3 ], [ 4, 5 ], [ 6, 7 ], [ 8, 9 ] ], ( 3, 7, 8, 4)( 9,13,14,10)(15,19)(16,17)(21,25)(22,23) ]
29-->26:[ ( 2, 9, 7)( 3, 8, 6)( 4,11,12, 5,10,13)(15,22,20)(16,21,19)(17,24,25,18,23,26), [ [ 5, 6 ],[ 11, 12 ],[ 7, 8 ],[ 1, 2 ],[ 3, 4 ],[ 9, 10 ],[ 13 ] ] ]
29-->23:[ ( 2, 6)( 4,12,11,10,13, 8, 5, 9)(15,19)(17,25,24,23,26,21,18,22), [ [ 2, 5, 8 ], [ 1, 6, 7 ], [ 4, 10, 12 ], [ 3, 9, 11 ], [ 13 ] ]]
30-->26:[ ( 2,26,14,20,11, 6,24,13,21,17,19,10,22,16, 9,23,12, 7, 4, 3)( 5,25,15, 8), [ [ 2 ],[ 4 ],[ 6 ],[ 8 ],[ 10 ],[ 12 ],[ 1, 3, 5, 7, 9, 11, 13 ] ]]
30-->25:[ ( 3,22,25, 8,13,16)( 4,20,21,23)( 5,26, 9,15, 6,24)( 7,11,12,14,18)(10,17), [ [ 1 ],[ 8, 12 ],[ 9, 13 ],[ 4, 6 ],[ 5, 7 ],[ 2, 10 ],[ 3, 11 ] ]]
30-->24:[ ( 3, 8,18,20,11,23, 6,10,17,22,12,26, 4, 9,15,21,13,24)( 5, 7,16,19,14,25), [ [ 1 ],[ 12, 13 ],[ 2, 3 ],[ 10, 11 ],[ 4, 5 ],[ 8, 9 ],[ 6, 7 ] ]]
30-->20:[ ( 3, 7,19,17,14,11, 6,10,24,20,15, 8,18, 9,25,22,21,23,16)( 5,13,12), [ [ 1 ], [ 2, 6, 8 ], [ 3, 7, 9 ], [ 4, 10, 12 ], [ 5, 11, 13 ] ] ]
31-->26:[ ( 2,14, 5,12, 7,10, 3, 9)( 4, 8,11, 6,13)(15,22)(16,21)(17,25)(18,26)(19,23,20,24), [ [ 5 ], [ 7 ], [ 6 ], [ 2 ], [ 4 ], [ 3 ], [ 1, 8, 9, 10, 11, 12, 13 ] ] ]
31-->25:[ ( 3,12,20,10, 6,13,19, 7, 4,14,21, 8, 5,11,22, 9)(15,17,16)(24,25,26), [ [ 1 ], [ 4, 5 ], [ 10, 11 ], [ 2, 3 ], [ 8, 9 ], [ 6, 7 ], [ 12, 13 ] ] ]
31-->21:[ ( 3, 6,12, 4, 5,13,11, 7,10, 8,14, 9)(15,17,24,20,22)(18,26,25,23)(19,21), [ [ 1 ], [ 2, 5, 6 ], [ 3, 4, 7 ], [ 8, 11, 12 ], [ 9, 10, 13 ] ] ]
32-->24:[ ( 3, 5)( 4, 6), [ [ 1 ], [ 2, 3 ], [ 4, 5 ], [ 6, 7 ], [ 8, 9 ], [ 10, 11 ], [ 12, 13 ] ] ]
32-->22:[ ( 3,13, 9,15,11, 7,21,17, 5)( 4,14,10,16,12, 8,22,18, 6)(19,23,25)(20,24,26), [ [ 1 ], [ 3, 6, 9 ], [ 2, 7, 8 ], [ 5, 11, 13 ], [ 4, 10, 12 ] ] ]
33-->30:[ ( 2, 3, 7,23,17,14)( 4,11,12, 8,24,13)( 5,15, 6,19,22,21,25, 9,20,26)(10,16), [ [ 13 ], [ 1, 12 ], [ 14, 25 ], [ 2, 11 ], [ 15, 24 ], [ 3, 10 ], [ 16, 23 ], [ 4, 9 ], [ 17, 22 ], [ 5, 8 ], [ 18, 21 ], [ 6, 7 ], [ 19, 20 ] ] ]
33-->29:[ ( 2, 8, 4)( 3,11)( 5, 6,13, 9,12,10, 7)(15,21,17)(16,24)(18,19,26,22,25,23,20), [ [ 3 ], [ 10 ], [ 7 ], [ 6 ], [ 4 ], [ 9 ], [ 1 ], [ 12 ], [ 11 ], [ 2 ], [ 8 ], [ 5 ], [ 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25 ] ] ]
33-->27:[ ( 2,15, 5,18, 8,21,10,17, 4,16,14)( 3,25,11,20,13,19,12,23)( 6,24, 7,26)( 9,22), [ [ 13 ], [ 14, 16, 22 ], [ 17, 23, 25 ], [ 20, 21, 24 ], [ 15, 18, 19 ], [ 1, 3, 9 ], [ 4, 10, 12 ], [ 7, 8, 11 ], [ 2, 5, 6 ] ] ]
34-->32:[ ( 2, 6,20,24,14)( 3, 7,23,17,11,13)( 4,12,10,18,16, 8,26)( 5,15)( 9,21,25), [ [ 13 ], [ 12, 25 ], [ 1, 14 ], [ 2, 15 ], [ 11, 24 ], [ 3, 16 ], [ 10, 23 ], [ 4, 17 ], [ 9, 22 ], [ 5, 18 ], [ 8, 21 ], [ 6, 19 ], [ 7, 20 ] ] ]
34-->30:[ ( 2, 4,12, 7,24,13, 3, 8,23,17,14)( 5,16,10,15, 6,20,26)( 9,19,22,21,25), [ [ 13 ], [ 1, 12 ], [ 14, 25 ], [ 2, 11 ], [ 15, 24 ], [ 3, 10 ], [ 16, 23 ], [ 4, 9 ], [ 17, 22 ], [ 5, 8 ], [ 18, 21 ], [ 6, 7 ], [ 19, 20 ] ] ]
34-->29:[ ( 2, 3, 4, 6,10, 9,11, 7,12, 5, 8,13)(15,16,17,19,23,22,24,20,25,18,21,26), [ [ 12 ], [ 1 ], [ 2 ], [ 11 ], [ 3 ], [ 10 ], [ 4 ], [ 9 ], [ 5 ], [ 8 ], [ 6 ], [ 7 ], [ 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25 ] ] ]
34-->28:[ ( 2, 8,20,23,13, 3,15,14)( 4, 6,16,21,26, 9,19,22,25,24,11, 5)( 7,17,12,18,10), [ [ 13 ], [ 4, 10, 12 ], [ 1, 3, 9 ], [ 17, 23, 25 ], [ 14, 16, 22 ], [ 2, 5, 6 ], [ 7, 8, 11 ], [ 15, 18, 19 ], [ 20, 21, 24 ] ] ]

Order 27: Groups: No. 498 to 502.
Fusions27:= [ [ 1, [ ] ], [ 2, [ 1 ] ], [ 3, [ 1 ] ],
[ 4 to 377, [ 1 ] ],
[ 378, [ 1 ] ], [ 379, [ 2 ] ], [ 380, [ 2, 3 ] ],
[ 381, [ 2, 3 ] ],[ 382, [ 2, 4 ] ], [ 383, [ 2, 4 ] ],
[ 384, [ 2 ] ], [ 385, [ 3 ] ], [ 386, [ 1 ] ], [ 387, [ 3 ] ],
[ 388, [ 379, 380 ] ], [ 389, [ 379, 384 ] ],
[ 390, [ 380, 385 ] ], [ 391, [ 380 ] ], [ 392, [ 380, 384 ] ],
[ 393, [ 380, 387 ] ], [ 394, [ 381 ] ], [ 395, [ 383 ] ],
[ 396, [ 4, 385 ] ], [ 397, [ 386 ] ], [ 398, [ 385, 387 ] ],
[ 399, [ 388, 391 ] ], [ 400, [ 388, 389, 392 ] ],
[ 401, [ 388, 393 ] ], [ 402, [ 379, 381, 387 ] ],
[ 403, [ 379, 383 ] ], [ 404, [ 390 ] ], [ 405, [ 380 ] ],
[ 406, [ 381, 390, 392 ] ], [ 407, [ 382, 383, 390, 396 ] ],
[ 408, [ 390, 393, 398 ] ], [ 409, [ 391, 393 ] ],
[ 410, [ 381, 384, 385, 386 ] ], [ 411, [ 383, 384 ] ],
[ 412, [ 392 ] ], [ 413, [ 380 ] ], [ 414, [ 380 ] ],
[ 415, [ 380 ] ], [ 416, [ 380, 386 ] ],
[ 417, [ 388, 390, 391 ] ], [ 418, [ 399, 401, 409 ] ],
[ 419, [ 400, 412 ] ], [ 420, [ 388, 413 ] ],
[ 421, [ 404, 406 ] ], [ 422, [ 392, 405 ] ],
[ 423, [ 404, 408 ] ], [ 424, [ 393, 405 ] ],
[ 425, [ 406, 412 ] ], [ 426, [ 390, 413 ] ],
[ 427, [ 391, 414 ] ], [ 428, [ 391, 414 ] ],
[ 429, [ 391, 415 ] ], [ 430, [ 391, 415 ] ],
[ 431, [ 391, 416 ] ], [ 432, [ 391, 416 ] ],
[ 433, [ 391, 392, 393 ] ], [ 434, [ 397, 410 ] ],
[ 435, [ 400, 406, 417 ] ], [ 436, [ 401, 408, 409, 417 ] ],
[ 437, [ 399, 400, 401, 433 ] ], [ 438, [ 421, 425 ] ],
[ 439, [ 404, 426 ] ], [ 440, [ 412, 422 ] ],
[ 441, [ 405, 413 ] ], [ 442, [ 406, 410 ] ],
[ 443, [ 406, 408, 433 ] ], [ 444, [ 396, 408 ] ],
[ 445, [ 394, 434 ] ], [ 446, [ 419, 425, 435 ] ],
[ 447, [ 417, 420, 426 ] ], [ 448, [ 407, 417 ] ],
[ 449, [ 402, 406, 417, 433 ] ], [ 450, [ 403, 407, 417 ] ],
[ 451, [ 389, 394, 398, 402, 410 ] ],
[ 452, [ 389, 395, 403, 411 ] ], [ 453, [ 421, 423, 443 ] ],
[ 454, [ 422, 424, 433 ] ], [ 455, [ 407, 423, 444 ] ],
[ 456, [ 434, 442 ] ], [ 457, [ 406, 407, 411 ] ],
[ 458, [ 399, 404, 417 ] ], [ 459, [ 399, 405 ] ],
[ 460, [ 435, 436, 437, 443 ] ], [ 461, [ 401, 414 ] ],
[ 462, [ 397, 401, 416 ] ], [ 463, [ 401, 415 ] ],
[ 464, [ 416, 421, 425, 442 ] ],
[ 465, [ 406, 414, 415, 422, 426 ] ], [ 466, [ 409, 412, 433 ] ],
[ 467, [ 409, 413 ] ] ], [ 468, [418, 423, 436, 458 ] ],
[ 469, [ 418, 424, 459 ] ], [ 470, [ 418, 419, 437, 466 ] ],
[ 471, [ 418, 420, 467 ] ], [ 472, [ 418, 427, 461 ] ],
[ 473, [ 418, 428, 461 ] ], [ 474, [ 418, 420, 467 ] ],
[ 475, [ 418, 430, 463 ] ], [ 476, [ 378, 418, 431, 462 ] ],
[ 477, [ 418, 432, 462 ] ], [ 478, [ 421, 435, 437, 449, 458 ] ],
[ 479, [ 422, 437, 459 ] ],
[ 480, [ 434, 435, 442, 443, 449, 451 ] ],
[ 481, [ 425, 436, 443, 449, 466 ] ], [ 482, [ 426, 436, 467 ] ],
[ 483, [ 410, 438, 464 ] ], [ 484, [ 438, 439, 440, 465 ] ],
[ 485, [ 441 ] ], [ 486, [ 453, 460, 468, 470, 478, 481 ] ],
[ 487, [ 447, 468, 482 ] ], [ 488, [ 454, 471, 479 ] ],
[ 489, [ 424, 441, 459 ] ], [ 490, [ 448, 450, 455 ] ],
[ 491, [ 445, 446, 451, 453, 456, 464, 480 ] ],
[ 492, [ 447, 449, 454, 465 ] ], [ 493, [ 446, 450, 452, 457 ] ],
[ 494, [ 448, 449, 453, 455, 457 ] ], [ 495, [ 448, 449, 454 ] ],
[ 496, [ 460, 462, 464, 478, 480, 481 ] ],
[ 497, [ 460, 461, 463, 465, 479, 482 ] ],
[ 498, [ 469, 471, 485, 489 ] ],
[ 499, [ 446, 472, 474, 478, 484, 486, 487, 488, 492, 497 ] ],
[ 500, [ 438, 472, 486, 490, 493, 494 ] ],
[ 501, [ 438, 440, 474, 476, 486, 488, 490, 495 ] ],
[ 502, [ 468, 481, 483, 491, 496 ] ] ];

Order 28: Groups: No. 182 to to 185.
The complete list has been worked out up to number 154, beyond that it may not be complete.
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# Remaining maximal fusions computed manually using ad hoc methods. # Some additional maximal fusions may exist, these have been verified.
[ 155, [ 113, 114, 149 ] ], [ 156, [ 115, 125, 126, 131, 133, 135, 142 ] ], [ 157, [ 117, 125, 127, 133, 143 ] ], [ 158, [ 98, 117, 128, 129, 134, 136, 142 ] ], [ 159, [ 115, 129, 130, 134, 143 ] ], [ 160, [ 137, 140, 144 ] ], [ 161, [ 103, 124, 137, 138 ] ], [ 162, [ 119, 139, 140 ] ], [ 163, [ 120, 139, 140 ] ], [ 164, [ 115, 160 ]], [165, [ 116, 141 ]], [ 166, [ 117, 160 ]], [ 167, [ 118, 138, 144 ]], [ 168, [ 131, 146, 152, 162 ]], [ 169, [ 132, 147, 153, 162 ]], [ 170, [ 133, 146, 152, 163]], [ 171, [ 134, 141, 147, 153, 163 ]], [ 172, [ 108, 152, 160 ]], [173, [ 126, 148, 165 ]], [ 174, [ 127, 148, 167 ] ], [ 175, [ 74, 109, 155 ] ], [ 176, [ 75, 110, 155 ]], [ 177, [ 128, 150, 165 ]], [ 178, [ 150, 153, 160 ]], [ 179, [ 130, 141, 150, 151, 167 ]], [ 180, [ 142, 160, 163, 165 ]], [ 181, [ 141, 143, 160, 161, 163, 167 ]], [ 182, [ 166, 171, 177, 178, 180 ]], [ 183, [ 159, 164, 171, 178, 179, 181 ]], [ 184, [ 156, 164, 168, 170, 172, 173, 180 ]], [ 185, [ 154, 157, 166, 170, 172, 174, 181 ]] ];

Order 29: Group: No. 26.
Fusions29:= [ [ 1, [ ] ], [ 2, [ 1 ] ], [ 3, [ 1 ] ], [ 4, [ 1 ] ], [ 5, [ 1 ] ], [ 6, [ 1 ] ], [ 7, [ 1 ] ], [ 8, [ 1 ] ], [ 9, [ 1 ] ], [ 10, [ 1 ] ], [ 11, [ 1 ] ], [ 12, [ 1 ] ], [ 13, [ 1 ] ], [ 14, [ 1 ] ], [ 15, [ 1 ] ], [ 16, [ 1 ] ], [ 17, [ 1 ] ], [ 18, [ 1 ] ], [ 19, [ 1 ] ], [ 20, [ 1 ] ], [ 21, [ 1 ] ], [ 22, [ 1 ] ], [ 23, [ 22 ] ], [ 24, [ 1 ] ], [ 25, [ 22, 24 ] ], [ 26, [ 23, 25 ] ] ];

Order 30: Groups: No. 240 to 243. (Partial results.)
Fusions30:= [ [ 1, [ ] ], [ 2, [ 1 ] ], [ 3, [ 1 ] ], [ 4, [ 1 ] ], [ 5, [ 1 ] ], [ 6, [ 1 ] ], [ 7, [ 1 ] ], [ 8, [ 3 ] ], [ 9, [ 2, 5 ] ], [ 10, [ 2, 6 ] ], [ 11, [ 2 ] ], [ 12, [ 2, 7 ] ], [ 13, [ 2 ] ], [ 14, [ 4 ] ], [ 15, [ 3, 5 ] ], [ 16, [ 3 ] ], [ 17, [ 3, 6 ] ], [ 18, [ 3, 7 ] ], [ 19, [ 6 ] ], [ 20, [ 4, 6 ] ], [ 21, [ 4, 5 ] ], [ 22, [ 4, 7 ] ], [ 23, [ 5 ] ], [ 24, [ 7 ] ], [ 25, [ 7 ] ], [ 26, [ 7 ] ], [ 27, [ 7 ] ], [ 28, [ 7 ] ], [ 29, [ 7 ] ], [ 30, [ 7 ] ], [ 31, [ 6 ] ], [ 32, [ 8, 15 ] ], [ 33, [ 8, 16 ] ], [ 34, [ 8, 18 ] ], [ 35, [ 9, 15 ] ], [ 36, [ 9 ] ], [ 37, [ 10 ] ], [ 38, [ 10, 20 ] ], [ 39, [ 9, 10 ] ], [ 40, [ 9, 11 ] ], [ 41, [ 9, 23 ] ], [ 42, [ 11 ] ], [ 43, [ 10, 31 ] ], [ 44, [ 14, 20 ] ], [ 45, [ 14, 22 ] ], [ 46, [ 15, 23 ] ], [ 47, [ 15, 18 ] ], [ 48, [ 18, 22 ] ], [ 49, [ 18, 24 ] ], [ 50, [ 18 ] ], [ 51, [ 24 ] ], [ 52, [ 19, 31 ] ], [ 53, [ 22 ] ], [ 54, [ 20, 22 ] ], [ 55, [ 20, 31 ] ], [ 56, [ 14 ] ], [ 57, [ 32, 46 ] ], [ 58, [ 32, 34, 47 ] ], [ 59, [ 34, 50 ] ], [ 60, [ 8, 17, 31 ] ], [ 61, [ 17, 35, 39 ] ], [ 62, [ 35, 40 ] ], [ 63, [ 35, 41, 46 ] ], [ 64, [ 12, 35, 4 [ 65, [ 36, 41 ] ], [ 66, [ 21, 38, 39 ] ], [ 67, [ 12, 38, 54 ] ], [ 68, [ 37, 43 ] ], [ 69, [ 38, 43, 55 ] ], [ 70, [ 40, 42 ] ], [ 71, [ 39 ] ], [ 72, [ 11, 12, 24, 27 ] ], [ 73, [ 12, 30 ] ], [ 74, [ 12, 25 ] ], [ 75, [ 45, 53 ] ], [ 76, [ 44, 45, 54 ] ], [ 77, [ 14, 21, 23 ] ], [ 78, [ 44, 55 ] ], [ 79, [ 21, 47, 48 ] ], [ 80, [ 47, 49 ] ], [ 81, [ 27, 47 ] ], [ 82, [ 16, 17, 19 ] ], [ 83, [ 48 ] ], [ 84, [ 17, 48, 54 ] ], [ 85, [ 23 ] ], [ 86, [ 32, 35 ] ], [ 87, [ 32, 35, 36 ] ], [ 88, [ 44, 56 ] ], [ 89, [ 45, 56 ] ], [ 90, [ 34, 49 ] ], [ 91, [ 34, 48, 53 ] ], [ 92, [ 37, 38, 44 ] ], [ 93, [ 19, 38, 44 ] ], [ 94, [ 37 ] ], [ 95, [ 62 ] ], [ 96, [ 61, 71 ] ], [ 97, [ 36, 40 ] ], [ 98, [ 36, 39, 43 ] ], [ 99, [ 4, 42 ] ], [ 100, [ 37, 39, 41 ] ], [ 101, [ 70 ] ], [ 102, [ 66, 71 ] ], [ 103, [ 41, 85 ] ], [ 104, [ 45, 48, 50 ] ], [ 105, [ 50 ] ], [ 106, [ 79, 83 ] ], [ 107, [ 79, 83 ] ],[ 108, [ 46, 47, 50 ] ], [ 109, [ 16, 47, 50 ] ], [ 110, [ 46, 85 ] ], [ 111, [ 83, 84 ] ], [ 112, [ 53, 54 ] ], [ 113, [ 53, 54, 55 ] ], [ 114, [ 57, 63, 86 ] ], [ 115, [ 58, 64, 86 ] ], [ 116, [ 57, 63, 65, 87 ] ], [ 117, [ 58, 64, 87 ] ], [ 118, [ 75, 89 ] ], [ 119, [ 76, 88, 89 ] ], [ 120, [ 78, 88 ] ], [ 121, [ 59, 105 ] ], [ 122, [ 58, 80, 90 ] ], [ 123, [ 58, 80, 90 ] ], [ 124, [ 58, 81 ] ], [ 125, [ 58, 79, 91 ] ], [ 126, [ 58, 81 ] ], [ 127, [ 57, 58, 59, 108 ] ], [ 128, [ 33, 58, 59, 109 ] ], [ 129, [ 57, 110 ] ], [ 130, [ 67, 76, 92 ] ], [ 131, [ 55, 68, 69, 78, 92 ] ], [ 132, [ 67, 76, 93 ] ], [ 133, [ 52, 69, 78, 93 ] ], [ 134, [ 68, 94 ] ], [ 135, [ 61, 63, 100 ] ], [ 136, [ 61, 64, 66, 67, 79, 84 ] ], [ 137, [ 62, 64, 72, 80, 81 ] ], [ 138, [ 66, 69, 98 ] ], [ 139, [ 63, 64, 108 ] ], [ 140, [ 64, 109 ] ], [ 141, [ 63, 103, 110 ] ], [ 142, [ 65, 103 ] ], [ 143, [ 21, 70, 99 ] ], [ 144, [ 67, 112 ] ], [ 145, [ 67, 69, 113 ] ], [ 146, [ 76, 84, 104 ] ], [ 147, [ 75, 76, 112 ] ], [ 148, [ 75, 76, 78, 113 ] ], [ 149, [ 62, 87, 97 ] ], [ 150, [ 60, 61, 87, 98 ] ], [ 151, [ 33, 52, 60, 82 ] ], [ 152, [ 84, 91, 112 ] ], [ 153, [ 60, 84, 91, 113 ] ], [ 154, [ 66, 77, 92, 100 ] ], [ 155, [ 100 ] ], [ 156, [ 101, 143 ] ], [ 157, [ 104 ] ], [ 158, [ 77, 79, 104, 108 ] ], [ 159, [ 79, 104, 109 ] ], [ 160, [ 114, 115, 127, 139 ] ], [ 161, [ 115, 128, 140 ] ], [ 162, [ 114, 129, 141 ] ], [ 163, [ 116, 117, 127, 139 ] ], [ 164, [ 36, 117, 128, 140 ] ], [ 165, [ 116, 129, 141, 142 ] ], [ 166, [ 118, 119, 147 ] ], [ 167, [ 118, 119, 120, 148 ] ], [ 168, [ 56, 77, 85 ] ], [ 169, [ 59, 75, 83, 91, 104 ] ], [ 170, [ 112, 130, 144, 147 ] ], [ 171, [ 130, 131, 145, 148 ] ], [ 172, [ 132, 144, 147 ] ], [ 173, [ 132, 133, 145, 148 ] ], [ 174, [ 135, 155 ] ], [ 175, [ 81, 106, 111, 136 ] ], [ 176, [ 96, 102, 106, 111, 136 ] ], [ 177, [ 97, 101 ] ], [ 178, [ 65, 68, 71, 98, 100 ] ], [ 179, [ 146, 157 ] ], [ 180, [ 88, 92 ] ], [ 181, [ 88, 92, 94 ] ], [ 182, [ 89, 104, 105 ] ], [ 183, [ 154, 155 ] ], [ 184, [ 16, 101 ] ], [ 185, [ 94, 100, 103 ] ], [ 186, [ 157, 158 ] ], [ 187, [ 157, 159 ] ], [ 188, [ 105, 108 ] ], [ 189, [ 105, 108, 110 ] ],
# Remaining maximal fusions computed manually using ad hoc methods. # Some additional maximal fusions may exist, these have been verified.
[ 190, [ 119, 130, 180 ]], [ 191, [ 120, 131, 180 ]], [ 192, [ 119, 130, 181 ]], [ 193, [ 120, 131, 134, 181 ]], [ 194, [ 115, 125, 136, 144, 152 ]], [ 195, [ 115, 123, 126, 137 ]], [ 196, [ 117, 122, 124, 137, 149 ]], [ 197, [ 96, 116, 135, 150, 178 ]], [ 198, [ 117, 125, 136, 138, 145, 150, 153 ]], [ 199, [ 119, 146, 182 ]], [ 200, [ 106, 125, 127, 158, 169 ]], [ 201, [ 106, 125, 128, 159, 169 ]], [ 202, [ 111, 146, 147, 152, 169 ]], [ 203, [ 111, 146, 148, 153, 169 ]], [ 204, [ 121, 127, 188 ]], [ 205, [ 121, 127, 129, 189 ]], [ 206, [ 130, 135, 136, 139, 154, 158 ]], [ 207, [ 132, 136, 140, 159 ]], [ 208, [ 102, 131, 138, 154, 178 ]], [ 209, [ 135, 141, 185 ]], [ 210, [ 139, 188 ]], [ 211, [ 139, 141, 189 ]], [ 212, [ 166, 170, 190 ]]; [ 213, [ 167, 171, 190, 191 ]], [ 214, [ 166, 170, 192 ]], [ 215, [ 167, 171, 192, 193 ]], [ 216, [ 160, 204, 210 ]], [ 217, [ 160, 162, 205, 211 ]], [ 218, [ 163, 204, 210 ]], [ 219, [ 163, 165, 205, 211 ]], [ 220, [ 154, 168, 181, 185 ]], [ 221, [ 158, 182, 188 ]], [ 222, [ 158, 168, 182, 189 ]], [ 223, [ 118, 121, 157, 169, 182 ]], [ 224, [ 174, 179, 183, 186, 206 ]], [ 225, [ 179, 186, 206 ]], [ 226, [ 143, 156, 177, 184 ]], [ 227, [ 155, 178, 185 ]], [ 228, [ 166, 179, 199, 202, 223 ]], [ 229, [ 179, 199, 203, 223 ]], [ 230, [ 160, 170, 175, 194, 200, 202, 206 ]], [ 231, [ 161, 172, 176, 194, 201, 202, 207 ]], [ 232, [ 163, 171, 176, 197, 198, 200, 203, 206, 208 ]], [ 233, [ 151, 164, 173, 175, 198, 201, 203, 207 ]], [ 234, [ 165, 174, 197, 209, 227 ]], [ 235, [ 186, 200, 204, 221, 223 ]], [ 236, [ 186, 200, 205, 222, 223 ]], [ 237, [ 190, 199, 206, 210, 221 ]], [ 238, [ 192, 199, 206, 209, 211, 220, 222 ]], [ 239, [ 193, 208, 220, 227 ]], [ 240, [ 214, 217, 225, 228, 230, 236, 238 ]], [ 241, [ 213, 218, 225, 232, 235, 237 ]], [ 242, [ 212, 216, 224, 228, 230, 235, 237 ]], [ 243, [ 215, 219, 224, 229, 232, 234, 236, 238, 239 ]] ];