About this representation

Group J3
Group generators Standard generators
Number of points 43605
Primitivity information Primitive
Transitivity degree 1
Rank 57
Suborbit lengths 1, 8, 12, 32, 963, 1282, 1924, 3848, 5764, 115232
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 43605
2A 85 221760
3A 90 314505
3B 27 314526
4A 5 240, 410880
5A 0 58721
5B 0 58721
6A 10 240, 325, 67240
8A 1 22, 420, 85440
9A 0 39, 94842
9B 0 39, 94842
9C 0 39, 94842
10A 0 517, 104352
10B 0 517, 104352
12A 2 24, 3, 420, 612, 123620
15A 0 518, 152901
15B 0 518, 152901
17A 0 172565
17B 0 172565
19A 0 192295
19B 0 192295

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