About this representation

Group Co3
Group generators Standard generators
Number of points 11178
Primitivity information Primitive
Transitivity degree 1
Rank 5
Suborbit lengths 1, 352, 1100, 4125, 5600
Character 1 + 23 + 275 + 2024 + 8855
Point stabiliser HS
Contributed by Not recorded

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This representation is available in the following formats:

MeatAxe a b
MeatAxe binary a b
GAP a b
GAP a, b
Magma a, b

On conjugacy classes

Conjugacy class Fixed points Cycle type
1A 11178
2A 378 25400
2B 66 25556
3A 0 33726
3B 81 33699
3C 0 33726
4A 6 2186, 42700
4B 30 2174, 42700
5A 3 52235
5B 13 52233
6A 0 3126, 61800
6B 0 3126, 61800
6C 9 236, 3123, 61788
6D 3 239, 321, 61839
6E 0 322, 61852
7A 6 71596
8A 12 29, 487, 81350
8B 0 215, 487, 81350
8C 4 213, 487, 81350
9A 0 91242
9B 0 91242
10A 3 575, 101080
10B 1 26, 513, 101110
11A 2 111016
11B 2 111016
12A 0 32, 662, 12900
12B 0 310, 658, 12900
12C 3 23, 3, 418, 661, 12894
14A 0 23, 754, 14771
15A 0 3, 15745
15B 1 34, 516, 15739
18A 0 942, 18600
20A 1 2, 5, 1037, 20540
20B 1 2, 5, 1037, 20540
21A 0 32, 21532
22A 0 2, 116, 22505
22B 0 2, 116, 22505
23A 0 23486
23B 0 23486
24A 0 34, 63, 1229, 24450
24B 0 65, 1229, 24450
30A 0 3, 1525, 30360

Checks applied

Check Description Date Checked by Result
Semi-presentation Check against a semi-presentation. If this fails, then the representation is not on standard generators, and may generate the wrong group. Note that the semi-presentation itself is not checked here. Jul 4, 2006 certify.pl version 0.05 Pass
Order Check that the elements generate a group of the correct order. Jul 4, 2006 permanalyse version 0.03 Pass
Number of points Check whether the permutation representation is acting on the stated number of points. Jul 4, 2006 certify.pl version 0.05 Pass
Files exist Check whether files exist (where stated). Jul 4, 2006 certify.pl version 0.05 Pass