About this representation
| Group
| He
|
| Group generators
| Standard generators
|
| Number of points
| 29155
|
| Primitivity information
| Primitive
|
| Transitivity degree
| 1
|
| Rank
| 12
|
| Suborbit lengths
| 1, 90, 120, 384, 9602, 1440, 2160, 28802, 5760, 11520
|
| Character
| 1 + 51ab + 680 + 2.1275a + 1920 + 4352 + 7650a + 11900
|
| Contributed by
| Not recorded
|
Download
This representation is available in the following formats:
On conjugacy classes
| Conjugacy class |
Fixed points |
Cycle type |
| 1A
| 29155
|
|
| 2A
| 651
| 214252
|
| 2B
| 147
| 214504
|
| 3A
| 112
| 39681
|
| 3B
| 7
| 39716
|
| 4A
| 35
| 2308, 47126
|
| 4B
| 19
| 264, 47252
|
| 4C
| 7
| 270, 47252
|
| 5A
| 5
| 55830
|
| 6A
| 12
| 250, 3213, 64734
|
| 6B
| 3
| 22, 348, 64834
|
| 7A
| 0
| 74165
|
| 7B
| 0
| 74165
|
| 7C
| 0
| 74165
|
| 7D
| 0
| 74165
|
| 7E
| 0
| 74165
|
| 8A
| 1
| 23, 435, 83626
|
| 10A
| 1
| 22, 5130, 102850
|
| 12A
| 2
| 25, 311, 425, 6101, 122367
|
| 12B
| 1
| 2, 36, 4, 621, 122417
|
| 14A
| 0
| 793, 142036
|
| 14B
| 0
| 793, 142036
|
| 14C
| 0
| 721, 142072
|
| 14D
| 0
| 721, 142072
|
| 15A
| 2
| 3, 522, 151936
|
| 17A
| 0
| 171715
|
| 17B
| 0
| 171715
|
| 21A
| 0
| 716, 211383
|
| 21B
| 0
| 716, 211383
|
| 21C
| 0
| 7, 211388
|
| 21D
| 0
| 7, 211388
|
| 28A
| 0
| 75, 1444, 281018
|
| 28B
| 0
| 75, 1444, 281018
|
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
|