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Frobenius groups
Groups G = K ⋊ H whose complement H meets each of its conjugates trivially.
order
group
splitting
351
C
3
3
⋊C
13
#66856
C
3
3
⋊
C
13
354
D
177
#67057
C
3
×C
59
⋊
C
2
355
C
71
⋊C
5
#67059
C
71
⋊
C
5
356
#67063
C
89
⋊
C
4
358
D
179
#67068
C
179
⋊
C
2
362
D
181
#67235
C
181
⋊
C
2
363
C
11
2
⋊C
3
#67238
C
11
2
⋊
C
3
366
D
61
⋊C
3
#67252
C
61
⋊
C
2
×C
3
366
D
183
#67256
C
3
×C
61
⋊
C
2
370
D
185
#67305
C
5
×C
37
⋊
C
2
372
C
2
2
⋊(C
31
⋊C
3
)
#67318
C
2
2
×C
31
⋊
C
3
374
D
187
#67326
C
11
×C
17
⋊
C
2
378
D
189
#67352
C
7
×C
27
⋊
C
2
378
C
3
⋊D
63
#67389
C
3
×C
7
×C
9
⋊
C
2
378
C
3
⋊(C
3
⋊D
21
)
#67406
C
3
3
×C
7
⋊
C
2
381
C
127
⋊C
3
#67420
C
127
⋊
C
3
382
D
191
#67422
C
191
⋊
C
2
386
D
193
#87596
C
193
⋊
C
2
388
#87604
C
97
⋊
C
4
390
D
195
#87618
C
3
×C
5
×C
13
⋊
C
2
392
#87656
C
7
2
⋊
C
8
392
#87658
C
7
2
⋊
Q
8
394
D
197
#87666
C
197
⋊
C
2
398
D
199
#87700
C
199
⋊
C
2
399
#87704
C
7
×C
19
⋊
C
3
399
#87705
C
7
×C
19
⋊
C
3
402
D
67
⋊C
3
#87929
C
67
⋊
C
2
×C
3
402
D
201
#87933
C
3
×C
67
⋊
C
2
404
#87938
C
101
⋊
C
4
405
C
3
4
⋊C
5
#87955
C
3
4
⋊
C
5
406
D
29
⋊C
7
#87957
C
29
⋊
C
2
×C
7
406
D
203
#87961
C
7
×C
29
⋊
C
2
410
D
41
⋊C
5
#88011
C
41
⋊
C
2
×C
5
410
D
205
#88015
C
5
×C
41
⋊
C
2
414
D
207
#88025
C
9
×C
23
⋊
C
2
414
C
3
⋊D
69
#88031
C
3
2
×C
23
⋊
C
2
417
C
139
⋊C
3
#88269
C
139
⋊
C
3
418
D
209
#88273
C
11
×C
19
⋊
C
2
422
D
211
#88318
C
211
⋊
C
2
426
D
213
#88340
C
3
×C
71
⋊
C
2
430
D
215
#88351
C
5
×C
43
⋊
C
2
434
D
217
#89132
C
7
×C
31
⋊
C
2
436
#89137
C
109
⋊
C
4
438
D
73
⋊C
3
#89141
C
73
⋊
C
2
×C
3
438
D
219
#89145
C
3
×C
73
⋊
C
2
442
D
221
#89214
C
13
×C
17
⋊
C
2
444
#3866⋊C
3
#89223
C
37
⋊
C
3
×C
4
444
C
2
2
⋊(C
37
⋊C
3
)
#89230
C
2
2
×C
37
⋊
C
3
446
D
223
#89236
C
223
⋊
C
2
448
C
4
3
⋊C
7
#89416
C
4
3
⋊
C
7
448
#401⋊C
7
#89417
#401
⋊
C
7
448
#90631
C
2
6
⋊
C
7
448
#90632
C
2
6
⋊
C
7
450
D
225
#90638
C
9
×C
25
⋊
C
2
450
C
3
⋊D
75
#90644
C
3
2
×C
25
⋊
C
2
450
C
5
⋊D
45
#90653
C
5
2
×C
9
⋊
C
2
450
C
3
⋊(C
3
⋊(C
5
⋊D
5
))
#90668
C
3
2
×C
5
2
⋊
C
2
452
#90673
C
113
⋊
C
4
453
C
151
⋊C
3
#90676
C
151
⋊
C
3
454
D
227
#90678
C
227
⋊
C
2
458
D
229
#90736
C
229
⋊
C
2
462
D
231
#90765
C
3
×C
7
×C
11
⋊
C
2
465
(C
31
⋊C
3
)⋊C
5
#90819
C
31
⋊
C
3
×C
5
466
D
233
#90823
C
233
⋊
C
2
468
#90866
C
3
2
×C
13
⋊
C
4
470
D
235
#90884
C
5
×C
47
⋊
C
2
471
C
157
⋊C
3
#90886
C
157
⋊
C
3
474
D
79
⋊C
3
#90901
C
79
⋊
C
2
×C
3
474
D
237
#90905
C
3
×C
79
⋊
C
2
478
D
239
#90922
C
239
⋊
C
2
482
D
241
#92139
C
241
⋊
C
2
484
#92150
C
11
2
⋊
C
4
486
D
243
#92156
C
243
⋊
C
2
486
C
9
⋊D
27
#92205
C
9
×C
27
⋊
C
2
486
C
3
⋊D
81
#92215
C
3
×C
81
⋊
C
2
486
C
3
⋊(C
9
⋊D
9
)
#92335
C
3
×C
9
2
⋊
C
2
486
C
3
⋊(C
3
⋊D
27
)
#92339
C
3
2
×C
27
⋊
C
2
486
C
3
⋊(C
3
⋊(C
3
⋊D
9
))
#92402
C
3
3
×C
9
⋊
C
2
486
C
3
⋊(C
3
⋊(C
3
⋊(C
3
⋊D
3
)))
#92415
C
3
5
⋊
C
2
489
C
163
⋊C
3
#92432
C
163
⋊
C
3
490
D
245
#92436
C
5
×C
49
⋊
C
2
490
C
5
⋊(C
7
⋊D
7
)
#92442
C
5
×C
7
2
⋊
C
2
494
D
247
#92460
C
13
×C
19
⋊
C
2
497
C
71
⋊C
7
#92508
C
71
⋊
C
7
498
D
249
#92512
C
3
×C
83
⋊
C
2
500
#92517
C
125
⋊
C
4
500
#92536
C
5
×C
25
⋊
C
4
500
#92538
C
5
×C
25
⋊
C
4
500
#92562
C
5
3
⋊
C
4
500
#92563
C
5
3
⋊
C
4
502
D
251
#92572
C
251
⋊
C
2
505
C
101
⋊C
5
#92777
C
101
⋊
C
5
506
AGL(1,𝔽
23
)
#92779
C
23
⋊
C
2
×C
11
506
D
253
#92783
C
11
×C
23
⋊
C
2
507
C
169
⋊C
3
#92785
C
169
⋊
C
3
507
#92788
C
13
2
⋊
C
3
507
#92789
C
13
2
⋊
C
3
510
D
255
#92802
C
3
×C
5
×C
17
⋊
C
2
514
D
257
#10587033
C
257
⋊
C
2
516
C
2
2
⋊(C
43
⋊C
3
)
#10587046
C
2
2
×C
43
⋊
C
3
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