About this representation

Group M24
Group generators Standard generators
Number of points 1771
Primitivity information Primitive
Transitivity degree 1
Rank 4
Suborbit lengths 1, 90, 240, 1440
Character 1 + 252 + 483 + 1035a
Point stabiliser 26:3.S6
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 1771
2A 91 2840
2B 51 2860
3A 16 3585
3B 7 3588
4A 11 240, 4420
4B 7 242, 4420
4C 7 222, 4430
5A 1 5354
6A 4 26, 329, 6278
6B 3 22, 316, 6286
7A 0 7253
7B 0 7253
8A 1 23, 421, 8210
10A 1 510, 10172
11A 0 11161
12A 2 2, 33, 43, 613, 12139
12B 1 2, 32, 4, 67, 12143
14A 0 713, 14120
14B 0 713, 14120
15A 1 53, 15117
15B 1 53, 15117
21A 0 7, 2184
21B 0 7, 2184
23A 0 2377
23B 0 2377

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