About this representation

Group HS
Group generators Standard generators
Number of points 5600
Distinguishing letter a
Primitivity information Primitive
Transitivity degree 1
Rank 9
Suborbit lengths 1, 55, 132, 165, 495, 660, 792, 1320, 1980
Point stabiliser M11
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 5600
2A 160 22720
2B 0 22800
3A 20 31860
4A 0 280, 41360
4B 0 280, 41360
4C 8 276, 41360
5A 0 51120
5B 0 51120
5C 5 51119
6A 0 210, 6930
6B 4 28, 352, 6904
7A 0 7800
8A 0 440, 8680
8B 4 22, 438, 8680
8C 0 24, 438, 8680
10A 0 532, 10544
10B 0 10560
11A 1 11509
11B 1 11509
12A 0 22, 44, 626, 12452
15A 0 54, 15372
20A 0 1016, 20272
20B 0 1016, 20272

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