About this representation

Group Fi22:2
Group generators Standard generators
Number of points 3510
Primitivity information Primitive
Transitivity degree 1
Rank 3
Suborbit lengths 1, 693, 2816
Contributed by Not recorded

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This representation is available in the following formats:

MeatAxe c d
MeatAxe binary c d
GAP c d
GAP c, d
Magma c, d

On conjugacy classes

Conjugacy class Fixed points Cycle type
1A 3510
2A 694 21408
2B 182 21664
2C 54 21728
3A 126 31128
3B 27 31161
3C 36 31158
3D 0 31170
4A 38 272, 4832
4B 30 276, 4832
4C 6 288, 4832
4D 6 224, 4864
4E 14 284, 4832
5A 10 5700
6A 46 240, 3216, 6456
6B 19 24, 3225, 6468
6C 11 28, 357, 6552
6D 14 256, 356, 6536
6E 10 213, 3228, 6465
6F 6 260, 316, 6556
6G 3 212, 317, 6572
6H 12 212, 314, 6572
6I 8 214, 358, 6550
6J 6 215, 316, 6571
6K 0 318, 6576
7A 3 7501
8A 6 216, 436, 8416
8B 6 216, 436, 8416
8C 2 22, 444, 8416
8D 2 22, 412, 8432
9A 6 37, 9387
9B 3 38, 9387
9C 0 9390
10A 4 23, 5138, 10281
10B 2 24, 536, 10332
11A 1 11319
12A 11 39, 44, 624, 12276
12B 2 26, 312, 428, 622, 12268
12C 2 26, 312, 428, 622, 12268
12D 6 24, 38, 428, 624, 12268
12E 3 3, 46, 68, 12286
12F 0 26, 32, 46, 66, 12286
12G 3 24, 3, 44, 628, 12276
12H 2 26, 34, 428, 626, 12268
12I 0 24, 310, 47, 624, 12275
12J 0 32, 68, 12288
13A 0 13270
14A 1 2, 799, 14201
15A 1 33, 525, 15225
16A 0 2, 4, 822, 16208
18A 4 2, 35, 6, 975, 18156
18B 1 2, 36, 6, 975, 18156
18C 2 22, 33, 62, 919, 18184
20A 0 2, 42, 56, 1015, 20166
21A 0 3, 718, 21161
22A 1 1163, 22128
24A 0 2, 32, 43, 65, 814, 1211, 24134
24B 0 2, 32, 43, 65, 814, 1211, 24134
30A 1 3, 59, 6, 108, 1543, 3091
2D 360 21575
2E 72 21719
2F 64 21723
4F 72 255, 4832
4G 40 271, 4832
4H 16 283, 4832
4I 8 287, 4832
4J 0 227, 4864
6L 36 245, 3108, 6510
6M 0 263, 3120, 6504
6N 9 29, 3117, 6522
6O 16 255, 316, 6556
6P 18 29, 3114, 6522
6Q 12 257, 320, 6554
6R 1 213, 321, 6570
6S 0 3120, 6525
6T 0 324, 6573
6U 6 215, 322, 6568
6V 4 216, 320, 6569
8E 8 215, 436, 8416
8F 8 215, 436, 8416
8G 4 2, 444, 8416
8H 0 23, 412, 8432
10C 10 570, 10315
10D 4 23, 512, 10344
10E 2 24, 514, 10343
12K 12 2, 320, 428, 618, 12268
12L 9 2, 321, 44, 618, 12276
12M 0 27, 324, 428, 616, 12268
12N 6 2, 322, 47, 618, 12275
12O 4 25, 312, 428, 622, 12268
12P 4 25, 34, 428, 626, 12268
12Q 1 25, 35, 44, 626, 12276
12R 4 22, 34, 47, 627, 12275
12S 2 23, 32, 47, 628, 12275
12T 0 69, 12288
14B 3 751, 14225
14C 1 2, 79, 14246
16B 2 4, 822, 16208
18D 0 23, 33, 62, 939, 18174
18E 3 32, 63, 939, 18174
18F 1 2, 64, 97, 18190
18G 0 98, 18191
20B 0 2, 42, 58, 1014, 20166
24C 2 32, 43, 65, 814, 1211, 24134
24D 2 32, 43, 65, 814, 1211, 24134
24E 1 2, 3, 42, 82, 1214, 24138
24F 1 2, 3, 42, 82, 1214, 24138
24G 0 43, 6, 83, 123, 24143
30B 1 33, 57, 109, 1521, 30102
30C 1 3, 53, 6, 1011, 153, 30111
36A 0 2, 33, 4, 97, 12, 186, 3692
42A 0 3, 149, 2117, 4272

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 4, 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