# Modular group algebras of finite representation type

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Nov 27th, 2013
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1. Counting the groups of finite representation type of order 2 = [ 2 ]
2.
3. Counting the groups of finite representation type of order 3 = [ 3 ]
4.
5. Counting the groups of finite representation type of order 4 = [ 2, 2 ]
6. Checking it in characteristic 2
7. C4
8. Of finite representation type: 1
9. Of infinite representation type: 1
10.
11. Counting the groups of finite representation type of order 5 = [ 5 ]
12.
13. Counting the groups of finite representation type of order 6 = [ 2, 3 ]
14.
15. Counting the groups of finite representation type of order 7 = [ 7 ]
16.
17. Counting the groups of finite representation type of order 8 = [ 2, 2, 2 ]
18. Checking it in characteristic 2
19. C8
20. Of finite representation type: 1
21. Of infinite representation type: 4
22.
23. Counting the groups of finite representation type of order 9 = [ 3, 3 ]
24. Checking it in characteristic 3
25. C9
26. Of finite representation type: 1
27. Of infinite representation type: 1
28.
29. Counting the groups of finite representation type of order 10 = [ 2, 5 ]
30.
31. Counting the groups of finite representation type of order 11 = [ 11 ]
32.
33. Counting the groups of finite representation type of order 12 = [ 2, 2, 3 ]
34. Checking it in characteristic 2
35. C3 : C4 C12
36. Of finite representation type: 2
37. Of infinite representation type: 3
38.
39. Counting the groups of finite representation type of order 13 = [ 13 ]
40.
41. Counting the groups of finite representation type of order 14 = [ 2, 7 ]
42.
43. Counting the groups of finite representation type of order 15 = [ 3, 5 ]
44.
45. Counting the groups of finite representation type of order 16 = [ 2, 2, 2, 2 ]
46. Checking it in characteristic 2
47. C16
48. Of finite representation type: 1
49. Of infinite representation type: 13
50.
51. Counting the groups of finite representation type of order 17 = [ 17 ]
52.
53. Counting the groups of finite representation type of order 18 = [ 2, 3, 3 ]
54. Checking it in characteristic 3
55. D18 C18
56. Of finite representation type: 2
57. Of infinite representation type: 3
58.
59. Counting the groups of finite representation type of order 19 = [ 19 ]
60.
61. Counting the groups of finite representation type of order 20 = [ 2, 2, 5 ]
62. Checking it in characteristic 2
63. C5 : C4 C20 C5 : C4
64. Of finite representation type: 3
65. Of infinite representation type: 2
66.
67. Counting the groups of finite representation type of order 21 = [ 3, 7 ]
68.
69. Counting the groups of finite representation type of order 22 = [ 2, 11 ]
70.
71. Counting the groups of finite representation type of order 23 = [ 23 ]
72.
73. Counting the groups of finite representation type of order 24 = [ 2, 2, 2, 3 ]
74. Checking it in characteristic 2
75. C3 : C8 C24
76. Of finite representation type: 2
77. Of infinite representation type: 13
78.
79. Counting the groups of finite representation type of order 25 = [ 5, 5 ]
80. Checking it in characteristic 5
81. C25
82. Of finite representation type: 1
83. Of infinite representation type: 1
84.
85. Counting the groups of finite representation type of order 26 = [ 2, 13 ]
86.
87. Counting the groups of finite representation type of order 27 = [ 3, 3, 3 ]
88. Checking it in characteristic 3
89. C27
90. Of finite representation type: 1
91. Of infinite representation type: 4
92.
93. Counting the groups of finite representation type of order 28 = [ 2, 2, 7 ]
94. Checking it in characteristic 2
95. C7 : C4 C28
96. Of finite representation type: 2
97. Of infinite representation type: 2
98.
99. Counting the groups of finite representation type of order 29 = [ 29 ]
100.
101. Counting the groups of finite representation type of order 30 = [ 2, 3, 5 ]
102.
103. Counting the groups of finite representation type of order 31 = [ 31 ]
104.
105. Counting the groups of finite representation type of order 32 = [ 2, 2, 2, 2, 2 ]
106. Checking it in characteristic 2
107. C32
108. Of finite representation type: 1
109. Of infinite representation type: 50
110.
111. Counting the groups of finite representation type of order 33 = [ 3, 11 ]
112.
113. Counting the groups of finite representation type of order 34 = [ 2, 17 ]
114.
115. Counting the groups of finite representation type of order 35 = [ 5, 7 ]
116.
117. Counting the groups of finite representation type of order 36 = [ 2, 2, 3, 3 ]
118. Checking it in characteristic 2
119. C9 : C4 C36 C3 x (C3 : C4) (C3 x C3) : C4 C12 x C3 (C3 x C3) : C4
120. Of finite representation type: 6
121. Of infinite representation type: 8
122. Checking it in characteristic 3
123. C9 : C4 C36 (C2 x C2) : C9 D36 C18 x C2
124. Of finite representation type: 5
125. Of infinite representation type: 9
126.
127. Counting the groups of finite representation type of order 37 = [ 37 ]
128.
129. Counting the groups of finite representation type of order 38 = [ 2, 19 ]
130.
131. Counting the groups of finite representation type of order 39 = [ 3, 13 ]
132.
133. Counting the groups of finite representation type of order 40 = [ 2, 2, 2, 5 ]
134. Checking it in characteristic 2
135. C5 : C8 C40 C5 : C8
136. Of finite representation type: 3
137. Of infinite representation type: 11
138.
139. Counting the groups of finite representation type of order 41 = [ 41 ]
140.
141. Counting the groups of finite representation type of order 42 = [ 2, 3, 7 ]
142.
143. Counting the groups of finite representation type of order 43 = [ 43 ]
144.
145. Counting the groups of finite representation type of order 44 = [ 2, 2, 11 ]
146. Checking it in characteristic 2
147. C11 : C4 C44
148. Of finite representation type: 2
149. Of infinite representation type: 2
150.
151. Counting the groups of finite representation type of order 45 = [ 3, 3, 5 ]
152. Checking it in characteristic 3
153. C45
154. Of finite representation type: 1
155. Of infinite representation type: 1
156.
157. Counting the groups of finite representation type of order 46 = [ 2, 23 ]
158.
159. Counting the groups of finite representation type of order 47 = [ 47 ]
160.
161. Counting the groups of finite representation type of order 48 = [ 2, 2, 2, 2, 3 ]
162. Checking it in characteristic 2
163. C3 : C16 C48
164. Of finite representation type: 2
165. Of infinite representation type: 50
166.
167. Counting the groups of finite representation type of order 49 = [ 7, 7 ]
168. Checking it in characteristic 7
169. C49
170. Of finite representation type: 1
171. Of infinite representation type: 1
172.
173. Counting the groups of finite representation type of order 50 = [ 2, 5, 5 ]
174. Checking it in characteristic 5
175. D50 C50
176. Of finite representation type: 2
177. Of infinite representation type: 3
178.
179. Counting the groups of finite representation type of order 51 = [ 3, 17 ]
180.
181. Counting the groups of finite representation type of order 52 = [ 2, 2, 13 ]
182. Checking it in characteristic 2
183. C13 : C4 C52 C13 : C4
184. Of finite representation type: 3
185. Of infinite representation type: 2
186.
187. Counting the groups of finite representation type of order 53 = [ 53 ]
188.
189. Counting the groups of finite representation type of order 54 = [ 2, 3, 3, 3 ]
190. Checking it in characteristic 3
191. D54 C54
192. Of finite representation type: 2
193. Of infinite representation type: 13
194.
195. Counting the groups of finite representation type of order 55 = [ 5, 11 ]
196.
197. Counting the groups of finite representation type of order 56 = [ 2, 2, 2, 7 ]
198. Checking it in characteristic 2
199. C7 : C8 C56
200. Of finite representation type: 2
201. Of infinite representation type: 11
202.
203. Counting the groups of finite representation type of order 57 = [ 3, 19 ]
204.
205. Counting the groups of finite representation type of order 58 = [ 2, 29 ]
206.
207. Counting the groups of finite representation type of order 59 = [ 59 ]
208.
209. Counting the groups of finite representation type of order 60 = [ 2, 2, 3, 5 ]
210. Checking it in characteristic 2
211. C5 x (C3 : C4) C3 x (C5 : C4) C15 : C4 C60 C3 x (C5 : C4) C15 : C4
212. Of finite representation type: 6
213. Of infinite representation type: 7
214.
215. Counting the groups of finite representation type of order 61 = [ 61 ]
216.
217. Counting the groups of finite representation type of order 62 = [ 2, 31 ]
218.
219. Counting the groups of finite representation type of order 63 = [ 3, 3, 7 ]
220. Checking it in characteristic 3
221. C7 : C9 C63
222. Of finite representation type: 2
223. Of infinite representation type: 2
224.
225. Counting the groups of finite representation type of order 64 = [ 2, 2, 2, 2, 2, 2 ]
226. Checking it in characteristic 2
227. C64
228. Of finite representation type: 1
229. Of infinite representation type: 266
230.
231. Counting the groups of finite representation type of order 65 = [ 5, 13 ]
232.
233. Counting the groups of finite representation type of order 66 = [ 2, 3, 11 ]
234.
235. Counting the groups of finite representation type of order 67 = [ 67 ]
236.
237. Counting the groups of finite representation type of order 68 = [ 2, 2, 17 ]
238. Checking it in characteristic 2
239. C17 : C4 C68 C17 : C4
240. Of finite representation type: 3
241. Of infinite representation type: 2
242.
243. Counting the groups of finite representation type of order 69 = [ 3, 23 ]
244.
245. Counting the groups of finite representation type of order 70 = [ 2, 5, 7 ]
246.
247. Counting the groups of finite representation type of order 71 = [ 71 ]
248.
249. Counting the groups of finite representation type of order 72 = [ 2, 2, 2, 3, 3 ]
250. Checking it in characteristic 2
251. C9 : C8 C72 C3 x (C3 : C8) (C3 x C3) : C8 C24 x C3 (C3 x C3) : C8 (C3 x C3) : C8
252. Of finite representation type: 7
253. Of infinite representation type: 43
254. Checking it in characteristic 3
255. C9 : C8 C72 Q8 : C9 C9 : Q8 C4 x D18 D72 C2 x (C9 : C4) (C18 x C2) : C2 C36 x C2 C9 x D8 C9 x Q8 ((C2 x C2) : C9) : C2 C2 x ((C2 x C2) : C9) C2 x C2 x D18 C18 x C2 x C2
256. Of finite representation type: 15
257. Of infinite representation type: 35
258.
259. Counting the groups of finite representation type of order 73 = [ 73 ]
260.
261. Counting the groups of finite representation type of order 74 = [ 2, 37 ]
262.
263. Counting the groups of finite representation type of order 75 = [ 3, 5, 5 ]
264. Checking it in characteristic 5
265. C75
266. Of finite representation type: 1
267. Of infinite representation type: 2
268.
269. Counting the groups of finite representation type of order 76 = [ 2, 2, 19 ]
270. Checking it in characteristic 2
271. C19 : C4 C76
272. Of finite representation type: 2
273. Of infinite representation type: 2
274.
275. Counting the groups of finite representation type of order 77 = [ 7, 11 ]
276.
277. Counting the groups of finite representation type of order 78 = [ 2, 3, 13 ]
278.
279. Counting the groups of finite representation type of order 79 = [ 79 ]
280.
281. Counting the groups of finite representation type of order 80 = [ 2, 2, 2, 2, 5 ]
282. Checking it in characteristic 2
283. C5 : C16 C80 C5 : C16
284. Of finite representation type: 3
285. Of infinite representation type: 49
286.
287. Counting the groups of finite representation type of order 81 = [ 3, 3, 3, 3 ]
288. Checking it in characteristic 3
289. C81
290. Of finite representation type: 1
291. Of infinite representation type: 14
292.
293. Counting the groups of finite representation type of order 82 = [ 2, 41 ]
294.
295. Counting the groups of finite representation type of order 83 = [ 83 ]
296.
297. Counting the groups of finite representation type of order 84 = [ 2, 2, 3, 7 ]
298. Checking it in characteristic 2
299. (C7 : C4) : C3 C4 x (C7 : C3) C7 x (C3 : C4) C3 x (C7 : C4) C21 : C4 C84
300. Of finite representation type: 6
301. Of infinite representation type: 9
302.
303. Counting the groups of finite representation type of order 85 = [ 5, 17 ]
304.
305. Counting the groups of finite representation type of order 86 = [ 2, 43 ]
306.
307. Counting the groups of finite representation type of order 87 = [ 3, 29 ]
308.
309. Counting the groups of finite representation type of order 88 = [ 2, 2, 2, 11 ]
310. Checking it in characteristic 2
311. C11 : C8 C88
312. Of finite representation type: 2
313. Of infinite representation type: 10
314.
315. Counting the groups of finite representation type of order 89 = [ 89 ]
316.
317. Counting the groups of finite representation type of order 90 = [ 2, 3, 3, 5 ]
318. Checking it in characteristic 3
319. C5 x D18 C9 x D10 D90 C90
320. Of finite representation type: 4
321. Of infinite representation type: 6
322.
323. Counting the groups of finite representation type of order 91 = [ 7, 13 ]
324.
325. Counting the groups of finite representation type of order 92 = [ 2, 2, 23 ]
326. Checking it in characteristic 2
327. C23 : C4 C92
328. Of finite representation type: 2
329. Of infinite representation type: 2
330.
331. Counting the groups of finite representation type of order 93 = [ 3, 31 ]
332.
333. Counting the groups of finite representation type of order 94 = [ 2, 47 ]
334.
335. Counting the groups of finite representation type of order 95 = [ 5, 19 ]
336.
337. Counting the groups of finite representation type of order 96 = [ 2, 2, 2, 2, 2, 3 ]
338. Checking it in characteristic 2
339. C3 : C32 C96
340. Of finite representation type: 2
341. Of infinite representation type: 229
342.
343. Counting the groups of finite representation type of order 97 = [ 97 ]
344.
345. Counting the groups of finite representation type of order 98 = [ 2, 7, 7 ]
346. Checking it in characteristic 7
347. D98 C98
348. Of finite representation type: 2
349. Of infinite representation type: 3
350.
351. Counting the groups of finite representation type of order 99 = [ 3, 3, 11 ]
352. Checking it in characteristic 3
353. C99
354. Of finite representation type: 1
355. Of infinite representation type: 1
356.
357. Counting the groups of finite representation type of order 100 = [ 2, 2, 5, 5 ]
358. Checking it in characteristic 2
359. C25 : C4 C100 C25 : C4 C5 x (C5 : C4) (C5 x C5) : C4 C20 x C5 C5 x (C5 : C4) (C5 x C5) : C4 (C5 x C5) : C4 (C5 x C5) : C4
360. Of finite representation type: 10
361. Of infinite representation type: 6
362. Checking it in characteristic 5
363. C25 : C4 C100 C25 : C4 D100 C50 x C2
364. Of finite representation type: 5
365. Of infinite representation type: 11
366.
367. Counting the groups of finite representation type of order 101 = [ 101 ]
368.
369. Counting the groups of finite representation type of order 102 = [ 2, 3, 17 ]
370.
371. Counting the groups of finite representation type of order 103 = [ 103 ]
372.
373. Counting the groups of finite representation type of order 104 = [ 2, 2, 2, 13 ]
374. Checking it in characteristic 2
375. C13 : C8 C104 C13 : C8
376. Of finite representation type: 3
377. Of infinite representation type: 11
378.
379. Counting the groups of finite representation type of order 105 = [ 3, 5, 7 ]
380.
381. Counting the groups of finite representation type of order 106 = [ 2, 53 ]
382.
383. Counting the groups of finite representation type of order 107 = [ 107 ]
384.
385. Counting the groups of finite representation type of order 108 = [ 2, 2, 3, 3, 3 ]
386. Checking it in characteristic 2
387. C27 : C4 C108 C3 x (C9 : C4) C9 x (C3 : C4) ((C3 x C3) : C4) : C3 (C9 : C4) : C3 (C9 x C3) : C4 ((C3 x C3) : C3) : C4 C36 x C3 C4 x ((C3 x C3) : C3) C4 x (C9 : C3) ((C3 x C3) : C3) : C4 C3 x \
388. C3 x (C3 : C4) C3 x ((C3 x C3) : C4) (C3 x C3 x C3) : C4 C12 x C3 x C3 C3 x ((C3 x C3) : C4) (C3 x C3 x C3) : C4
389. Of finite representation type: 18
390. Of infinite representation type: 27
391. Checking it in characteristic 3
392. C27 : C4 C108 (C2 x C2) : C27 D108 C54 x C2
393. Of finite representation type: 5
394. Of infinite representation type: 40
395.
396. Counting the groups of finite representation type of order 109 = [ 109 ]
397.
398. Counting the groups of finite representation type of order 110 = [ 2, 5, 11 ]
399.
400. Counting the groups of finite representation type of order 111 = [ 3, 37 ]
401.
402. Counting the groups of finite representation type of order 112 = [ 2, 2, 2, 2, 7 ]
403. Checking it in characteristic 2
404. C7 : C16 C112
405. Of finite representation type: 2
406. Of infinite representation type: 41
407.
408. Counting the groups of finite representation type of order 113 = [ 113 ]
409.
410. Counting the groups of finite representation type of order 114 = [ 2, 3, 19 ]
411.
412. Counting the groups of finite representation type of order 115 = [ 5, 23 ]
413.
414. Counting the groups of finite representation type of order 116 = [ 2, 2, 29 ]
415. Checking it in characteristic 2
416. C29 : C4 C116 C29 : C4
417. Of finite representation type: 3
418. Of infinite representation type: 2
419.
420. Counting the groups of finite representation type of order 117 = [ 3, 3, 13 ]
421. Checking it in characteristic 3
422. C13 : C9 C117
423. Of finite representation type: 2
424. Of infinite representation type: 2
425.
426. Counting the groups of finite representation type of order 118 = [ 2, 59 ]
427.
428. Counting the groups of finite representation type of order 119 = [ 7, 17 ]
429.
430. Counting the groups of finite representation type of order 120 = [ 2, 2, 2, 3, 5 ]
431. Checking it in characteristic 2
432. C5 x (C3 : C8) C3 x (C5 : C8) C15 : C8 C120 C3 x (C5 : C8) C15 : C8
433. Of finite representation type: 6
434. Of infinite representation type: 41
435.
436. Counting the groups of finite representation type of order 121 = [ 11, 11 ]
437. Checking it in characteristic 11
438. C121
439. Of finite representation type: 1
440. Of infinite representation type: 1
441.
442. Counting the groups of finite representation type of order 122 = [ 2, 61 ]
443.
444. Counting the groups of finite representation type of order 123 = [ 3, 41 ]
445.
446. Counting the groups of finite representation type of order 124 = [ 2, 2, 31 ]
447. Checking it in characteristic 2
448. C31 : C4 C124
449. Of finite representation type: 2
450. Of infinite representation type: 2
451.
452. Counting the groups of finite representation type of order 125 = [ 5, 5, 5 ]
453. Checking it in characteristic 5
454. C125
455. Of finite representation type: 1
456. Of infinite representation type: 4
457.
458. Counting the groups of finite representation type of order 126 = [ 2, 3, 3, 7 ]
459. Checking it in characteristic 3
460. (C7 : C9) : C2 C2 x (C7 : C9) C7 x D18 C9 x D14 D126 C126
461. Of finite representation type: 6
462. Of infinite representation type: 10
463.
464. Counting the groups of finite representation type of order 127 = [ 127 ]
465.
466. Counting the groups of finite representation type of order 128 = [ 2, 2, 2, 2, 2, 2, 2 ]
467. Checking it in characteristic 2
468. C128
469. Of finite representation type: 1
470. Of infinite representation type: 2327
471.
472. Counting the groups of finite representation type of order 129 = [ 3, 43 ]
473.
474. Counting the groups of finite representation type of order 130 = [ 2, 5, 13 ]
475.
476. Counting the groups of finite representation type of order 131 = [ 131 ]
477.
478. Counting the groups of finite representation type of order 132 = [ 2, 2, 3, 11 ]
479. Checking it in characteristic 2
480. C11 x (C3 : C4) C3 x (C11 : C4) C33 : C4 C132
481. Of finite representation type: 4
482. Of infinite representation type: 6
483.
484. Counting the groups of finite representation type of order 133 = [ 7, 19 ]
485.
486. Counting the groups of finite representation type of order 134 = [ 2, 67 ]
487.
488. Counting the groups of finite representation type of order 135 = [ 3, 3, 3, 5 ]
489. Checking it in characteristic 3
490. C135
491. Of finite representation type: 1
492. Of infinite representation type: 4
493.
494. Counting the groups of finite representation type of order 136 = [ 2, 2, 2, 17 ]
495. Checking it in characteristic 2
496. C17 : C8 C136 C17 : C8 C17 : C8
497. Of finite representation type: 4
498. Of infinite representation type: 11
499.
500. Counting the groups of finite representation type of order 137 = [ 137 ]
501.
502. Counting the groups of finite representation type of order 138 = [ 2, 3, 23 ]
503.
504. Counting the groups of finite representation type of order 139 = [ 139 ]
505.
506. Counting the groups of finite representation type of order 140 = [ 2, 2, 5, 7 ]
507. Checking it in characteristic 2
508. C7 x (C5 : C4) C5 x (C7 : C4) C35 : C4 C140 C7 x (C5 : C4) C35 : C4
509. Of finite representation type: 6
510. Of infinite representation type: 5
511.
512. Counting the groups of finite representation type of order 141 = [ 3, 47 ]
513.
514. Counting the groups of finite representation type of order 142 = [ 2, 71 ]
515.
516. Counting the groups of finite representation type of order 143 = [ 11, 13 ]
517.
518. Counting the groups of finite representation type of order 144 = [ 2, 2, 2, 2, 3, 3 ]
519. Checking it in characteristic 2
520. C9 : C16 C144 C3 x (C3 : C16) (C3 x C3) : C16 C48 x C3 (C3 x C3) : C16 (C3 x C3) : C16
521. Of finite representation type: 7
522. Of infinite representation type: 190
523. Checking it in characteristic 3
524. C9 : C16 C144 (C4 x C4) : C9 C9 : Q16 C8 x D18 C72 : C2 C72 : C2 D144 C2 x (C9 : C8) (C9 : C8) : C2 C4 x (C9 : C4) (C9 : C4) : C4 C36 : C4 (C36 x C2) : C2 (C9 : Q8) : C2 (C9 x D8) : C2 C9\
525. : Q16 (C9 x Q8) : C2 (C2 x (C9 : C4)) : C2 C36 x C4 C9 x ((C4 x C2) : C2) C9 x (C4 : C4) C72 x C2 C9 x (C8 : C2) C9 x D16 C9 x QD16 C9 x Q16 C2 . (((C2 x C2) : C9) : C2) = (Q8 : C9) . C2 (Q8 :\
526. C9) : C2 ((C2 x C2) : C9) : C4 C4 x ((C2 x C2) : C9) C2 x (Q8 : C9) (Q8 : C9) : C2 C2 x (C9 : Q8) C2 x C4 x D18 C2 x D72 (C36 x C2) : C2 D8 x D18 (C2 x (C9 : C4)) : C2 Q8 x D18 (C4 x D18) : C2\
527. C2 x C2 x (C9 : C4) C2 x ((C18 x C2) : C2) C36 x C2 x C2 C18 x D8 C18 x Q8 C9 x ((C4 x C2) : C2) C2 x (((C2 x C2) : C9) : C2) C2 x C2 x ((C2 x C2) : C9) (C2 x C2 x C2 x C2) : C9 C2 x C2 x C2 x D\
528. 18 C18 x C2 x C2 x C2
529. Of finite representation type: 52
530. Of infinite representation type: 145
531.
532. Counting the groups of finite representation type of order 145 = [ 5, 29 ]
533.
534. Counting the groups of finite representation type of order 146 = [ 2, 73 ]
535.
536. Counting the groups of finite representation type of order 147 = [ 3, 7, 7 ]
537. Checking it in characteristic 7
538. C49 : C3 C147
539. Of finite representation type: 2
540. Of infinite representation type: 4
541.
542. Counting the groups of finite representation type of order 148 = [ 2, 2, 37 ]
543. Checking it in characteristic 2
544. C37 : C4 C148 C37 : C4
545. Of finite representation type: 3
546. Of infinite representation type: 2
547.
548. Counting the groups of finite representation type of order 149 = [ 149 ]
549.
550. Counting the groups of finite representation type of order 150 = [ 2, 3, 5, 5 ]
551. Checking it in characteristic 5
552. C25 x S3 C3 x D50 D150 C150
553. Of finite representation type: 4
554. Of infinite representation type: 9
555.
556. Counting the groups of finite representation type of order 151 = [ 151 ]
557.
558. Counting the groups of finite representation type of order 152 = [ 2, 2, 2, 19 ]
559. Checking it in characteristic 2
560. C19 : C8 C152
561. Of finite representation type: 2
562. Of infinite representation type: 10
563.
564. Counting the groups of finite representation type of order 153 = [ 3, 3, 17 ]
565. Checking it in characteristic 3
566. C153
567. Of finite representation type: 1
568. Of infinite representation type: 1
569.
570. Counting the groups of finite representation type of order 154 = [ 2, 7, 11 ]
571.
572. Counting the groups of finite representation type of order 155 = [ 5, 31 ]
573.
574. Counting the groups of finite representation type of order 156 = [ 2, 2, 3, 13 ]
575. Checking it in characteristic 2
576. (C13 : C4) : C3 C4 x (C13 : C3) C13 x (C3 : C4) C3 x (C13 : C4) C39 : C4 C156 (C13 : C4) : C3 C3 x (C13 : C4) C39 : C4
577. Of finite representation type: 9
578. Of infinite representation type: 9
579.
580. Counting the groups of finite representation type of order 157 = [ 157 ]
581.
582. Counting the groups of finite representation type of order 158 = [ 2, 79 ]
583.
584. Counting the groups of finite representation type of order 159 = [ 3, 53 ]
585.
586. Counting the groups of finite representation type of order 160 = [ 2, 2, 2, 2, 2, 5 ]
587. Checking it in characteristic 2
588. C5 : C32 C160 C5 : C32
589. Of finite representation type: 3
590. Of infinite representation type: 235
591.
592. Counting the groups of finite representation type of order 161 = [ 7, 23 ]
593.
594. Counting the groups of finite representation type of order 162 = [ 2, 3, 3, 3, 3 ]
595. Checking it in characteristic 3
596. D162 C162
597. Of finite representation type: 2
598. Of infinite representation type: 53
599.
600. Counting the groups of finite representation type of order 163 = [ 163 ]
601.
602. Counting the groups of finite representation type of order 164 = [ 2, 2, 41 ]
603. Checking it in characteristic 2
604. C41 : C4 C164 C41 : C4
605. Of finite representation type: 3
606. Of infinite representation type: 2
607.
608. Counting the groups of finite representation type of order 165 = [ 3, 5, 11 ]
609.
610. Counting the groups of finite representation type of order 166 = [ 2, 83 ]
611.
612. Counting the groups of finite representation type of order 167 = [ 167 ]
613.
614. Counting the groups of finite representation type of order 168 = [ 2, 2, 2, 3, 7 ]
615. Checking it in characteristic 2
616. (C7 : C8) : C3 C8 x (C7 : C3) C7 x (C3 : C8) C3 x (C7 : C8) C21 : C8 C168
617. Of finite representation type: 6
618. Of infinite representation type: 51
619.
620. Counting the groups of finite representation type of order 169 = [ 13, 13 ]
621. Checking it in characteristic 13
622. C169
623. Of finite representation type: 1
624. Of infinite representation type: 1
625.
626. Counting the groups of finite representation type of order 170 = [ 2, 5, 17 ]
627.
628. Counting the groups of finite representation type of order 171 = [ 3, 3, 19 ]
629. Checking it in characteristic 3
630. C19 : C9 C171 C19 : C9
631. Of finite representation type: 3
632. Of infinite representation type: 2
633.
634. Counting the groups of finite representation type of order 172 = [ 2, 2, 43 ]
635. Checking it in characteristic 2
636. C43 : C4 C172
637. Of finite representation type: 2
638. Of infinite representation type: 2
639.
640. Counting the groups of finite representation type of order 173 = [ 173 ]
641.
642. Counting the groups of finite representation type of order 174 = [ 2, 3, 29 ]
643.
644. Counting the groups of finite representation type of order 175 = [ 5, 5, 7 ]
645. Checking it in characteristic 5
646. C175
647. Of finite representation type: 1
648. Of infinite representation type: 1
649.
650. Counting the groups of finite representation type of order 176 = [ 2, 2, 2, 2, 11 ]
651. Checking it in characteristic 2
652. C11 : C16 C176
653. Of finite representation type: 2
654. Of infinite representation type: 40
655.
656. Counting the groups of finite representation type of order 177 = [ 3, 59 ]
657.
658. Counting the groups of finite representation type of order 178 = [ 2, 89 ]
659.
660. Counting the groups of finite representation type of order 179 = [ 179 ]
661.
662. Counting the groups of finite representation type of order 180 = [ 2, 2, 3, 3, 5 ]
663. Checking it in characteristic 2
664. C5 x (C9 : C4) C9 x (C5 : C4) C45 : C4 C180 C9 x (C5 : C4) C45 : C4 C3 x C3 x (C5 : C4) C15 x (C3 : C4) C3 x (C15 : C4) C5 x ((C3 x C3) : C4) (C15 x C3) : C4 C60 x C3 C3 x C3 x (C5 : C4) C3 \
665. x (C15 : C4) (C15 x C3) : C4 C5 x ((C3 x C3) : C4) (C15 x C3) : C4 (C15 x C3) : C4
666. Of finite representation type: 18
667. Of infinite representation type: 19
668. Checking it in characteristic 3
669. C5 x (C9 : C4) C9 x (C5 : C4) C45 : C4 C180 C9 x (C5 : C4) C45 : C4 D10 x D18 C5 x ((C2 x C2) : C9) C18 x D10 C10 x D18 D180 C90 x C2
670. Of finite representation type: 12
671. Of infinite representation type: 25
672.
673. Counting the groups of finite representation type of order 181 = [ 181 ]
674.
675. Counting the groups of finite representation type of order 182 = [ 2, 7, 13 ]
676.
677. Counting the groups of finite representation type of order 183 = [ 3, 61 ]
678.
679. Counting the groups of finite representation type of order 184 = [ 2, 2, 2, 23 ]
680. Checking it in characteristic 2
681. C23 : C8 C184
682. Of finite representation type: 2
683. Of infinite representation type: 10
684.
685. Counting the groups of finite representation type of order 185 = [ 5, 37 ]
686.
687. Counting the groups of finite representation type of order 186 = [ 2, 3, 31 ]
688.
689. Counting the groups of finite representation type of order 187 = [ 11, 17 ]
690.
691. Counting the groups of finite representation type of order 188 = [ 2, 2, 47 ]
692. Checking it in characteristic 2
693. C47 : C4 C188
694. Of finite representation type: 2
695. Of infinite representation type: 2
696.
697. Counting the groups of finite representation type of order 189 = [ 3, 3, 3, 7 ]
698. Checking it in characteristic 3
699. C7 : C27 C189
700. Of finite representation type: 2
701. Of infinite representation type: 11
702.
703. Counting the groups of finite representation type of order 190 = [ 2, 5, 19 ]
704.
705. Counting the groups of finite representation type of order 191 = [ 191 ]
706.
707. Counting the groups of finite representation type of order 192 = [ 2, 2, 2, 2, 2, 2, 3 ]
708. Checking it in characteristic 2
709. C3 : C64 C192
710. Of finite representation type: 2
711. Of infinite representation type: 1541
712.
713. Counting the groups of finite representation type of order 193 = [ 193 ]
714.
715. Counting the groups of finite representation type of order 194 = [ 2, 97 ]
716.
717. Counting the groups of finite representation type of order 195 = [ 3, 5, 13 ]
718.
719. Counting the groups of finite representation type of order 196 = [ 2, 2, 7, 7 ]
720. Checking it in characteristic 2
721. C49 : C4 C196 C7 x (C7 : C4) (C7 x C7) : C4 C28 x C7 (C7 x C7) : C4
722. Of finite representation type: 6
723. Of infinite representation type: 6
724. Checking it in characteristic 7
725. C49 : C4 C196 D196 C98 x C2
726. Of finite representation type: 4
727. Of infinite representation type: 8
728.
729. Counting the groups of finite representation type of order 197 = [ 197 ]
730.
731. Counting the groups of finite representation type of order 198 = [ 2, 3, 3, 11 ]
732. Checking it in characteristic 3
733. C11 x D18 C9 x D22 D198 C198
734. Of finite representation type: 4
735. Of infinite representation type: 6
736.
737. Counting the groups of finite representation type of order 199 = [ 199 ]
738.
739. Counting the groups of finite representation type of order 200 = [ 2, 2, 2, 5, 5 ]
740. Checking it in characteristic 2
741. C25 : C8 C200 C25 : C8 C5 x (C5 : C8) (C5 x C5) : C8 C40 x C5 C5 x (C5 : C8) (C5 x C5) : C8 (C5 x C5) : C8 (C5 x C5) : C8 (C5 x C5) : C8
742. Of finite representation type: 11
743. Of infinite representation type: 41
744. Checking it in characteristic 5
745. C25 : C8 C200 C25 : C8 C25 : Q8 C4 x D50 D200 C2 x (C25 : C4) (C50 x C2) : C2 C100 x C2 C25 x D8 C25 x Q8 C2 x (C25 : C4) C2 x C2 x D50 C50 x C2 x C2
746. Of finite representation type: 14
747. Of infinite representation type: 38
748.
749. Counting the groups of finite representation type of order 201 = [ 3, 67 ]
750.
751. Counting the groups of finite representation type of order 202 = [ 2, 101 ]
752.
753. Counting the groups of finite representation type of order 203 = [ 7, 29 ]
754.
755. Counting the groups of finite representation type of order 204 = [ 2, 2, 3, 17 ]
756. Checking it in characteristic 2
757. C17 x (C3 : C4) C3 x (C17 : C4) C51 : C4 C204 C3 x (C17 : C4) C51 : C4
758. Of finite representation type: 6
759. Of infinite representation type: 6
760.
761. Counting the groups of finite representation type of order 205 = [ 5, 41 ]
762.
763. Counting the groups of finite representation type of order 206 = [ 2, 103 ]
764.
765. Counting the groups of finite representation type of order 207 = [ 3, 3, 23 ]
766. Checking it in characteristic 3
767. C207
768. Of finite representation type: 1
769. Of infinite representation type: 1
770.
771. Counting the groups of finite representation type of order 208 = [ 2, 2, 2, 2, 13 ]
772. Checking it in characteristic 2
773. C13 : C16 C208 C13 : C16
774. Of finite representation type: 3
775. Of infinite representation type: 48
776.
777. Counting the groups of finite representation type of order 209 = [ 11, 19 ]
778.
779. Counting the groups of finite representation type of order 210 = [ 2, 3, 5, 7 ]
780.
781. Counting the groups of finite representation type of order 211 = [ 211 ]
782.
783. Counting the groups of finite representation type of order 212 = [ 2, 2, 53 ]
784. Checking it in characteristic 2
785. C53 : C4 C212 C53 : C4
786. Of finite representation type: 3
787. Of infinite representation type: 2
788.
789. Counting the groups of finite representation type of order 213 = [ 3, 71 ]
790.
791. Counting the groups of finite representation type of order 214 = [ 2, 107 ]
792.
793. Counting the groups of finite representation type of order 215 = [ 5, 43 ]
794.
795. Counting the groups of finite representation type of order 216 = [ 2, 2, 2, 3, 3, 3 ]
796. Checking it in characteristic 2
797. C27 : C8 C216 C3 x (C9 : C8) C9 x (C3 : C8) ((C3 x C3) : C8) : C3 (C9 : C8) : C3 (C9 x C3) : C8 ((C3 x C3) : C3) : C8 C72 x C3 C8 x ((C3 x C3) : C3) C8 x (C9 : C3) ((C3 x C3) : C3) : C8 C3 x \
798. C3 x (C3 : C8) C3 x ((C3 x C3) : C8) (C3 x C3 x C3) : C8 C24 x C3 x C3 ((C3 x C3) : C3) : C8 C3 x ((C3 x C3) : C8) (C3 x C3 x C3) : C8 C3 x ((C3 x C3) : C8) (C3 x C3 x C3) : C8
799. Of finite representation type: 21
800. Of infinite representation type: 156
801. Checking it in characteristic 3
802. C27 : C8 C216 Q8 : C27 C27 : Q8 C4 x D54 D216 C2 x (C27 : C4) (C54 x C2) : C2 C108 x C2 C27 x D8 C27 x Q8 ((C2 x C2) : C27) : C2 C2 x ((C2 x C2) : C27) C2 x C2 x D54 C54 x C2 x C2
803. Of finite representation type: 15
804. Of infinite representation type: 162
805.
806. Counting the groups of finite representation type of order 217 = [ 7, 31 ]
807.
808. Counting the groups of finite representation type of order 218 = [ 2, 109 ]
809.
810. Counting the groups of finite representation type of order 219 = [ 3, 73 ]
811.
812. Counting the groups of finite representation type of order 220 = [ 2, 2, 5, 11 ]
813. Checking it in characteristic 2
814. (C11 : C5) : C4 C4 x (C11 : C5) C11 x (C5 : C4) C5 x (C11 : C4) C55 : C4 C220 C11 x (C5 : C4) C55 : C4
815. Of finite representation type: 8
816. Of infinite representation type: 7
817.
818. Counting the groups of finite representation type of order 221 = [ 13, 17 ]
819.
820. Counting the groups of finite representation type of order 222 = [ 2, 3, 37 ]
821.
822. Counting the groups of finite representation type of order 223 = [ 223 ]
823.
824. Counting the groups of finite representation type of order 224 = [ 2, 2, 2, 2, 2, 7 ]
825. Checking it in characteristic 2
826. C7 : C32 C224
827. Of finite representation type: 2
828. Of infinite representation type: 195
829.
830. Counting the groups of finite representation type of order 225 = [ 3, 3, 5, 5 ]
831. Checking it in characteristic 3
832. C225 (C5 x C5) : C9 C45 x C5
833. Of finite representation type: 3
834. Of infinite representation type: 3
835. Checking it in characteristic 5
836. C225 C75 x C3
837. Of finite representation type: 2
838. Of infinite representation type: 4
839.
840. Counting the groups of finite representation type of order 226 = [ 2, 113 ]
841.
842. Counting the groups of finite representation type of order 227 = [ 227 ]
843.
844. Counting the groups of finite representation type of order 228 = [ 2, 2, 3, 19 ]
845. Checking it in characteristic 2
846. (C19 : C4) : C3 C4 x (C19 : C3) C19 x (C3 : C4) C3 x (C19 : C4) C57 : C4 C228
847. Of finite representation type: 6
848. Of infinite representation type: 9
849.
850. Counting the groups of finite representation type of order 229 = [ 229 ]
851.
852. Counting the groups of finite representation type of order 230 = [ 2, 5, 23 ]
853.
854. Counting the groups of finite representation type of order 231 = [ 3, 7, 11 ]
855.
856. Counting the groups of finite representation type of order 232 = [ 2, 2, 2, 29 ]
857. Checking it in characteristic 2
858. C29 : C8 C232 C29 : C8
859. Of finite representation type: 3
860. Of infinite representation type: 11
861.
862. Counting the groups of finite representation type of order 233 = [ 233 ]
863.
864. Counting the groups of finite representation type of order 234 = [ 2, 3, 3, 13 ]
865. Checking it in characteristic 3
866. (C13 : C9) : C2 C2 x (C13 : C9) C13 x D18 C9 x D26 D234 C234
867. Of finite representation type: 6
868. Of infinite representation type: 10
869.
870. Counting the groups of finite representation type of order 235 = [ 5, 47 ]
871.
872. Counting the groups of finite representation type of order 236 = [ 2, 2, 59 ]
873. Checking it in characteristic 2
874. C59 : C4 C236
875. Of finite representation type: 2
876. Of infinite representation type: 2
877.
878. Counting the groups of finite representation type of order 237 = [ 3, 79 ]
879.
880. Counting the groups of finite representation type of order 238 = [ 2, 7, 17 ]
881.
882. Counting the groups of finite representation type of order 239 = [ 239 ]
883.
884. Counting the groups of finite representation type of order 240 = [ 2, 2, 2, 2, 3, 5 ]
885. Checking it in characteristic 2
886. C5 x (C3 : C16) C3 x (C5 : C16) C15 : C16 C240 C3 x (C5 : C16) C15 : C16
887. Of finite representation type: 6
888. Of infinite representation type: 202
889.
890. Counting the groups of finite representation type of order 241 = [ 241 ]
891.
892. Counting the groups of finite representation type of order 242 = [ 2, 11, 11 ]
893. Checking it in characteristic 11
894. D242 C242
895. Of finite representation type: 2
896. Of infinite representation type: 3
897.
898. Counting the groups of finite representation type of order 243 = [ 3, 3, 3, 3, 3 ]
899. Checking it in characteristic 3
900. C243
901. Of finite representation type: 1
902. Of infinite representation type: 66
903.
904. Counting the groups of finite representation type of order 244 = [ 2, 2, 61 ]
905. Checking it in characteristic 2
906. C61 : C4 C244 C61 : C4
907. Of finite representation type: 3
908. Of infinite representation type: 2
909.
910. Counting the groups of finite representation type of order 245 = [ 5, 7, 7 ]
911. Checking it in characteristic 7
912. C245
913. Of finite representation type: 1
914. Of infinite representation type: 1
915.
916. Counting the groups of finite representation type of order 246 = [ 2, 3, 41 ]
917.
918. Counting the groups of finite representation type of order 247 = [ 13, 19 ]
919.
920. Counting the groups of finite representation type of order 248 = [ 2, 2, 2, 31 ]
921. Checking it in characteristic 2
922. C31 : C8 C248
923. Of finite representation type: 2
924. Of infinite representation type: 10
925.
926. Counting the groups of finite representation type of order 249 = [ 3, 83 ]
927.
928. Counting the groups of finite representation type of order 250 = [ 2, 5, 5, 5 ]
929. Checking it in characteristic 5
930. D250 C250
931. Of finite representation type: 2
932. Of infinite representation type: 13
933.
934. Counting the groups of finite representation type of order 251 = [ 251 ]
935.
936. Counting the groups of finite representation type of order 252 = [ 2, 2, 3, 3, 7 ]
937. Checking it in characteristic 2
938. (C7 : C9) : C4 C4 x (C7 : C9) C7 x (C9 : C4) C9 x (C7 : C4) C63 : C4 C252 C3 x ((C7 : C4) : C3) (C3 : C4) x (C7 : C3) (C21 : C4) : C3 C12 x (C7 : C3) C3 x C3 x (C7 : C4) C21 x (C3 : C4) C3 x \
939. (C21 : C4) C7 x ((C3 x C3) : C4) (C21 x C3) : C4 C84 x C3 C7 x ((C3 x C3) : C4) (C21 x C3) : C4
940. Of finite representation type: 18
941. Of infinite representation type: 28
942. Checking it in characteristic 3
943. (C7 : C9) : C4 C4 x (C7 : C9) C7 x (C9 : C4) C9 x (C7 : C4) C63 : C4 C252 C2 x ((C7 : C9) : C2) D14 x D18 C2 x C2 x (C7 : C9) C7 x ((C2 x C2) : C9) (C14 x C2) : C9 C18 x D14 C14 x D18 D252 \
944. C126 x C2
945. Of finite representation type: 15
946. Of infinite representation type: 31
947.
948. Counting the groups of finite representation type of order 253 = [ 11, 23 ]
949.
950. Counting the groups of finite representation type of order 254 = [ 2, 127 ]
951.
952. Counting the groups of finite representation type of order 255 = [ 3, 5, 17 ]
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