About this representation

Group McL
Group generators Standard generators
Number of points 2025
Distinguishing letter b
Primitivity information Primitive
Transitivity degree 1
Rank 4
Suborbit lengths 1, 330, 462, 1232
Character 1 + 22 + 252 + 1750
Point stabiliser M22
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 2025
2A 105 2960
3A 0 3675
3B 27 3666
4A 9 248, 4480
5A 0 5405
5B 5 5404
6A 0 335, 6320
6B 3 212, 334, 6316
7A 2 7289
7B 2 7289
8A 1 24, 424, 8240
9A 0 9225
9B 0 9225
10A 0 521, 10192
11A 1 11184
11B 1 11184
12A 0 33, 616, 12160
14A 0 2, 715, 14137
14B 0 2, 715, 14137
15A 0 15135
15B 0 15135
30A 0 157, 3064
30B 0 157, 3064

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