| 1 |
G ≤ Sym(1600) |
rank 4, on cosets of L3(3).2 (1st max.) |
| 2 |
G ≤ Sym(1755) |
rank 5, on cosets of 2.[28]:5:4 (3rd max.) |
| 3 |
G ≤ Sym(2304) |
rank 7, on cosets of L2(25) (4th max.) |
| 4 |
G ≤ Sym(2925) |
rank 6, on cosets of 22.[28]:S3 (5th max.) |
| 5 |
G ≤ Sym(12480) |
rank 24, on cosets of A6.22 (7th max.) |
| 6 |
G ≤ Sym(14976) |
rank 25, on cosets of 52:4A4 (8th max.) |
| 7 |
G ≤ GL(26,2) |
character 26a |
| 8 |
G ≤ GL(246,2) |
character 246a |
| 9 |
G ≤ GL(26a,3) |
character 26a |
| 10 |
G ≤ GL(26b,3) |
character 26b |
| 11 |
G ≤ GL(54,3) |
character 27ab |
| 12 |
G ≤ GL(77,3) |
character 77a |
| 13 |
G ≤ GL(124a,3) |
character 124a |
| 14 |
G ≤ GL(124b,3) |
character 124b |
| 15 |
G ≤ GL(2048a,4) |
character 2048a |
| 16 |
G ≤ GL(27a,5) |
character 27a |
| 17 |
G ≤ GL(27b,5) |
character 27b |
| 18 |
G ≤ GL(52,5) |
character 26ab |
| 19 |
G ≤ GL(78,5) |
character 78a |
| 20 |
G ≤ GL(218,5) |
character 109ab |
| 21 |
G ≤ GL(27a,9) |
character 27a |
| 22 |
G ≤ GL(27b,9) |
character 27b |
| 23 |
G ≤ GL(27a,13) |
character 27a |
| 24 |
G ≤ GL(27b,13) |
character 27b |
| 25 |
G ≤ GL(52,13) |
character 26ab |
| 26 |
G ≤ GL(78,13) |
character 78a |
| 27 |
G ≤ GL(26a,25) |
character 26a |
| 28 |
G ≤ GL(26b,25) |
character 26b |
| 29 |
G ≤ GL(109a,25) |
character 109a |
| 30 |
G ≤ GL(109b,25) |
character 109b |
| 31 |
G ≤ GL(26,169) |
character 26a |
| 32 |
G ≤ GL(52,ℤ) |
character 26ab |
| 33 |
G ≤ GL(78,ℤ) |
character 78a |