About this representation

Group Co3
Group generators Standard generators
Number of points 128800
Primitivity information Primitive
Transitivity degree 1
Rank 6
Suborbit lengths 1, 495, 2673, 32076, 40095, 53460
Character 1+275+5544+8855+23000+91125
Point stabiliser 35:(2 × M11)
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 128800
2A 1120 263840
2B 232 264284
3A 10 342930
3B 91 342903
3C 28 342924
4A 160 2480, 431920
4B 32 2544, 431920
5A 0 525760
5B 10 525758
6A 10 3370, 621280
6B 4 23, 3372, 621279
6C 7 242, 3371, 621266
6D 7 242, 375, 621414
6E 4 212, 376, 621424
7A 0 718400
8A 0 216, 4272, 815960
8B 8 212, 4272, 815960
8C 4 214, 4272, 815960
9A 1 33, 914310
9B 1 33, 914310
10A 0 5224, 1012768
10B 2 24, 546, 1012856
11A 1 1111709
11B 1 1111709
12A 4 23, 352, 6159, 1210640
12B 2 24, 310, 6180, 1210640
12C 1 23, 353, 421, 6159, 1210633
14A 0 7160, 149120
15A 0 52, 158586
15B 1 33, 518, 158580
18A 1 3, 6, 9124, 187093
20A 0 532, 1096, 206384
20B 0 532, 1096, 206384
21A 0 74, 216132
22A 1 1121, 225844
22B 1 1121, 225844
23A 0 235600
23B 0 235600
24A 0 2, 42, 65, 1290, 245320
24B 2 32, 42, 64, 1290, 245320
30A 0 52, 1574, 304256

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 5, 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