About this representation

Group J3
Group generators Standard generators
Number of points 14688
Distinguishing letter b
Primitivity information Primitive
Transitivity degree 1
Rank 14
Suborbit lengths 1, 285, 342, 380, 5702, 8552, 11402, 17103, 3420
Character 1+85ab+1140aa+1215ab+1615+1920abc+2432
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 14688
2A 96 27296
3A 0 34896
3B 27 34887
4A 0 248, 43648
5A 3 52937
5B 3 52937
6A 0 332, 62432
8A 0 424, 81824
9A 3 38, 91629
9B 3 38, 91629
9C 3 38, 91629
10A 1 2, 519, 101459
10B 1 2, 519, 101459
12A 0 616, 121216
15A 0 3, 15979
15B 0 3, 15979
17A 0 17864
17B 0 17864
19A 1 19773
19B 1 19773

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