About this representation

Group McL
Group generators Standard generators
Number of points 7128
Primitivity information Primitive
Transitivity degree 1
Rank 5
Suborbit lengths 1, 252, 750, 2625, 3500
Character 1 + 22 + 252 + 1750 + 5103
Point stabiliser U3(5)
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 7128
2A 168 23480
3A 0 32376
3B 27 32367
4A 12 278, 41740
5A 3 51425
5B 3 51425
6A 0 356, 61160
6B 3 212, 355, 61156
7A 2 71018
7B 2 71018
8A 2 25, 439, 8870
9A 0 9792
9B 0 9792
10A 3 533, 10696
11A 0 11648
11B 0 11648
12A 0 34, 626, 12580
14A 0 2, 724, 14497
14B 0 2, 724, 14497
15A 0 3, 15475
15B 0 3, 15475
30A 0 3, 1511, 30232
30B 0 3, 1511, 30232

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