About this representation

Group J1
Group generators Standard generators
Number of points 1463
Primitivity information Primitive
Transitivity degree 1
Rank 22
Suborbit lengths 1, 12, 152, 202, 609, 1207
Character 1+56ab+76aa+77aa+120abc+133aa+209aa
Point stabiliser A5 × 2
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 1463
2A 31 2716
3A 5 3486
5A 3 5292
5B 3 5292
6A 1 22, 310, 6238
7A 0 7209
10A 1 2, 56, 10143
10B 1 2, 56, 10143
11A 0 11133
15A 0 3, 5, 1597
15B 0 3, 5, 1597
19A 0 1977
19B 0 1977
19C 0 1977

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