About this representation

Group M24
Group generators Standard generators
Number of points 759
Primitivity information Primitive
Transitivity degree 1
Rank 4
Suborbit lengths 1, 30, 280, 448
Character 1 + 23 + 252 + 483
Point stabiliser 24:A8 = 24:L4(2)
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 759
2A 71 2344
2B 15 2372
3A 21 3246
3B 0 3253
4A 7 232, 4172
4B 11 230, 4172
4C 3 26, 4186
5A 4 5151
6A 5 28, 322, 6112
6B 0 35, 6124
7A 3 7108
7B 3 7108
8A 1 25, 415, 886
10A 0 22, 53, 1074
11A 0 1169
12A 1 22, 32, 44, 610, 1256
12B 0 3, 62, 1262
14A 1 2, 710, 1449
14B 1 2, 710, 1449
15A 1 3, 54, 1549
15B 1 3, 54, 1549
21A 0 3, 2136
21B 0 3, 2136
23A 0 2333
23B 0 2333

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