About this representation
| Group
| He
|
| Group generators
| Standard generators
|
| Number of points
| 8330
|
| Primitivity information
| Primitive
|
| Transitivity degree
| 1
|
| Rank
| 7
|
| Suborbit lengths
| 1, 105, 720, 8402, 1344, 4480
|
| Character
| 1 + 51ab + 680 + 1275a + 1920 + 4352
|
| Contributed by
| Not recorded
|
Download
This representation is available in the following formats:
On conjugacy classes
| Conjugacy class |
Fixed points |
Cycle type |
| 1A
| 8330
|
|
| 2A
| 346
| 23992
|
| 2B
| 42
| 24144
|
| 3A
| 77
| 32751
|
| 3B
| 8
| 32774
|
| 4A
| 22
| 2162, 41996
|
| 4B
| 18
| 212, 42072
|
| 4C
| 2
| 220, 42072
|
| 5A
| 5
| 51665
|
| 6A
| 13
| 232, 3111, 61320
|
| 6B
| 0
| 24, 314, 61380
|
| 7A
| 7
| 71189
|
| 7B
| 7
| 71189
|
| 7C
| 0
| 71190
|
| 7D
| 0
| 71190
|
| 7E
| 0
| 71190
|
| 8A
| 2
| 410, 81036
|
| 10A
| 1
| 22, 569, 10798
|
| 12A
| 1
| 26, 37, 416, 652, 12660
|
| 12B
| 0
| 36, 42, 64, 12690
|
| 14A
| 3
| 22, 749, 14570
|
| 14B
| 3
| 22, 749, 14570
|
| 14C
| 0
| 76, 14592
|
| 14D
| 0
| 76, 14592
|
| 15A
| 2
| 3, 515, 15550
|
| 17A
| 0
| 17490
|
| 17B
| 0
| 17490
|
| 21A
| 0
| 711, 21393
|
| 21B
| 0
| 711, 21393
|
| 21C
| 1
| 32, 7, 21396
|
| 21D
| 1
| 32, 7, 21396
|
| 28A
| 1
| 2, 4, 73, 1423, 28285
|
| 28B
| 1
| 2, 4, 73, 1423, 28285
|
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
|