About this representation

Group M23
Group generators Standard generators
Number of points 506
Primitivity information Primitive
Transitivity degree 1
Rank 4
Suborbit lengths 1, 15, 210, 280
Character 1 + 22 + 230 + 253
Point stabiliser A8
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 506
2A 42 2232
3A 11 3165
4A 6 218, 4116
5A 1 5101
6A 3 24, 313, 676
7A 2 772
7B 2 772
8A 0 23, 49, 858
11A 0 1146
11B 0 1146
14A 0 2, 76, 1433
14B 0 2, 76, 1433
15A 1 52, 1533
15B 1 52, 1533
23A 0 2322
23B 0 2322

Checks applied

Check Description Date Checked by Result
Presentation Check against the relations in a presentation. If this test passes, then the group is of the correct isomorphism type, and the generators are those stated. Note that the presentation itself is not checked here. Aug 2, 2006 certify.pl version 0.05 Pass
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 18, 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