About this representation

Group J3
Group generators Standard generators
Number of points 20520
Primitivity information Primitive
Transitivity degree 1
Rank 22
Suborbit lengths 1, 1022, 153, 272, 3063, 6123, 8163, 12244, 24484
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 20520
2A 120 210200
3A 0 36840
3B 27 36831
4A 12 254, 45100
5A 0 54104
5B 0 54104
6A 0 340, 63400
8A 2 25, 427, 82550
9A 3 38, 92277
9B 3 38, 92277
9C 3 38, 92277
10A 0 524, 102040
10B 0 524, 102040
12A 0 34, 618, 121700
15A 0 151368
15B 0 151368
17A 1 171207
17B 1 171207
19A 0 191080
19B 0 191080

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