Guest User

Modular group algebras of finite representation type

a guest
Nov 27th, 2013
78
Never
Not a member of Pastebin yet? Sign Up, it unlocks many cool features!
  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 ]
RAW Paste Data