About this representation

Group J3
Group generators Standard generators
Number of points 17442
Primitivity information Primitive
Transitivity degree 1
Rank 19
Suborbit lengths 1, 5, 20, 80, 96, 120, 320, 4802, 9606, 1440, 28803
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 17442
2A 50 28696
3A 72 35790
3B 27 35805
4A 6 222, 44348
5A 2 53488
5B 2 53488
6A 8 232, 314, 62888
8A 0 23, 411, 82174
9A 0 39, 91935
9B 0 39, 91935
9C 0 39, 91935
10A 0 2, 510, 101739
10B 0 2, 510, 101739
12A 0 24, 32, 416, 66, 121444
15A 2 514, 151158
15B 2 514, 151158
17A 0 171026
17B 0 171026
19A 0 19918
19B 0 19918

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