About this representation

Group J3
Group generators Standard generators
Number of points 26163
Primitivity information Primitive
Transitivity degree 1
Rank 27
Suborbit lengths 1, 10, 80, 120, 192, 3202, 480, 640, 96011, 19207
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 26163
2A 131 213016
3A 45 38706
3B 0 38721
4A 7 262, 46508
5A 3 55232
5B 3 55232
6A 5 220, 342, 64332
8A 1 23, 431, 83254
9A 0 92907
9B 0 92907
9C 0 92907
10A 1 2, 526, 102603
10B 1 2, 526, 102603
12A 1 22, 32, 410, 620, 122166
15A 0 3, 59, 151741
15B 0 3, 59, 151741
17A 0 171539
17B 0 171539
19A 0 191377
19B 0 191377

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