About this representation

Group Co3
Group generators Standard generators
Number of points 37950
Primitivity information Primitive
Transitivity degree 1
Rank 8
Suborbit lengths 1, 224, 324, 1680, 45362, 8505, 18144
Character 1 + 2.275 + 5544 + 8855 + 23000
Point stabiliser U4(3).(22)133
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 37950
2A 750 218600
2B 198 218876
3A 15 312645
3B 105 312615
3C 0 312650
4A 130 2310, 49300
4B 42 2354, 49300
5A 0 57590
5B 15 57587
6A 15 3245, 66200
6B 3 26, 3249, 66198
6C 9 248, 3247, 66184
6D 9 248, 363, 66276
6E 0 366, 66292
7A 3 75421
8A 4 219, 4177, 84650
8B 16 213, 4177, 84650
8C 4 219, 4177, 84650
9A 0 35, 94215
9B 3 34, 94215
10A 0 5150, 103720
10B 3 26, 539, 103774
11A 0 113450
11B 0 113450
12A 7 24, 341, 6102, 123100
12B 3 26, 313, 6116, 123100
12C 1 24, 343, 424, 6102, 123092
14A 1 2, 7107, 142657
15A 0 53, 152529
15B 0 35, 521, 152522
18A 0 3, 62, 983, 182066
20A 0 526, 1062, 201860
20B 0 526, 1062, 201860
21A 0 3, 211807
22A 0 1118, 221716
22B 0 1118, 221716
23A 0 231650
23B 0 231650
24A 1 2, 3, 43, 66, 1258, 241550
24B 1 2, 35, 43, 64, 1258, 241550
30A 0 53, 1549, 301240

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