Mod-2-Cohomology of U3(4), a group of order 62400

About the group Ring generators Ring relations Completion information Restriction maps

General information on the group

  • U3(4) is a group of order 62400.
  • The group order factors as 26 · 3 · 52 · 13.
  • The group is defined by Group([(1,2)(3,5)(4,7)(6,10)(8,12)(9,13)(11,16)(14,20)(15,21)(17,24)(18,25)(19,27)(22,31)(23,32)(26,35)(28,37)(29,38)(30,40)(33,44)(34,42)(36,47)(39,51)(41,43)(45,55)(46,52)(48,57)(49,58)(50,59)(53,62)(54,60)(56,61)(63,64),(1,3,6)(2,4,8)(5,9,14)(7,11,17)(10,15,22)(12,18,26)(13,19,28)(16,23,33)(20,29,39)(21,30,41)(25,34,45)(27,36,48)(31,42,53)(32,43,54)(35,46,56)(37,49,57)(38,50,60)(40,52,47)(51,61,58)(55,63,65)(59,64,62)]).
  • It is non-abelian.
  • It has 2-Rank 2.
  • The centre of a Sylow 2-subgroup has rank 2.
  • Its Sylow 2-subgroup has a unique conjugacy class of maximal elementary abelian subgroups, which is of rank 2.

Structure of the cohomology ring

This cohomology ring is isomorphic to the cohomology ring of a subgroup, namely H*(SmallGroup(960,5748); GF(2)).

General information

  • The cohomology ring is of dimension 2 and depth 2.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    (1  +  t3  +  t6) · (1  −  2·t  +  3·t2  −  5·t3  +  7·t4  −  6·t5  +  9·t6  −  10·t7  +  11·t8  −  12·t9  +  11·t10  −  11·t11  +  11·t12  −  12·t13  +  11·t14  −  10·t15  +  9·t16  −  6·t17  +  7·t18  −  5·t19  +  3·t20  −  2·t21  +  t22)
    ( − 1  +  t)2 · (1  −  t  +  t2) · (1  +  t  +  t2) · (1  +  t2)2 · (1  −  t2  +  t4) · (1  +  t4)2 · (1  −  t4  +  t8)
  • The a-invariants are -∞,-∞,-2. They were obtained using the filter regular HSOP of the Hilbert-Poincaré test.
  • The filter degree type of any filter regular HSOP is [-1, -2, -2].

About the group Ring generators Ring relations Completion information Restriction maps

Ring generators

The cohomology ring has 55 minimal generators of maximal degree 27:

  1. a_5_0, a nilpotent element of degree 5
  2. a_5_1, a nilpotent element of degree 5
  3. a_5_2, a nilpotent element of degree 5
  4. a_6_0, a nilpotent element of degree 6
  5. a_6_1, a nilpotent element of degree 6
  6. a_6_2, a nilpotent element of degree 6
  7. a_6_3, a nilpotent element of degree 6
  8. a_7_0, a nilpotent element of degree 7
  9. a_7_1, a nilpotent element of degree 7
  10. a_8_0, a nilpotent element of degree 8
  11. a_8_1, a nilpotent element of degree 8
  12. a_8_2, a nilpotent element of degree 8
  13. a_8_3, a nilpotent element of degree 8
  14. a_9_0, a nilpotent element of degree 9
  15. a_9_1, a nilpotent element of degree 9
  16. a_9_2, a nilpotent element of degree 9
  17. a_11_0, a nilpotent element of degree 11
  18. a_11_1, a nilpotent element of degree 11
  19. a_12_0, a nilpotent element of degree 12
  20. a_12_1, a nilpotent element of degree 12
  21. a_12_2, a nilpotent element of degree 12
  22. a_12_3, a nilpotent element of degree 12
  23. a_13_0, a nilpotent element of degree 13
  24. a_13_1, a nilpotent element of degree 13
  25. a_15_0, a nilpotent element of degree 15
  26. a_15_1, a nilpotent element of degree 15
  27. c_16_0, a Duflot element of degree 16
  28. a_17_0, a nilpotent element of degree 17
  29. a_17_1, a nilpotent element of degree 17
  30. a_18_0, a nilpotent element of degree 18
  31. a_18_1, a nilpotent element of degree 18
  32. a_18_2, a nilpotent element of degree 18
  33. a_18_3, a nilpotent element of degree 18
  34. a_19_0, a nilpotent element of degree 19
  35. a_19_1, a nilpotent element of degree 19
  36. a_19_2, a nilpotent element of degree 19
  37. a_19_3, a nilpotent element of degree 19
  38. a_20_0, a nilpotent element of degree 20
  39. a_20_1, a nilpotent element of degree 20
  40. a_20_2, a nilpotent element of degree 20
  41. a_20_3, a nilpotent element of degree 20
  42. a_21_3, a nilpotent element of degree 21
  43. a_21_4, a nilpotent element of degree 21
  44. a_23_2, a nilpotent element of degree 23
  45. a_23_3, a nilpotent element of degree 23
  46. c_24_4, a Duflot element of degree 24
  47. c_24_5, a Duflot element of degree 24
  48. a_25_0, a nilpotent element of degree 25
  49. a_25_1, a nilpotent element of degree 25
  50. a_26_0, a nilpotent element of degree 26
  51. a_26_1, a nilpotent element of degree 26
  52. a_26_2, a nilpotent element of degree 26
  53. a_26_3, a nilpotent element of degree 26
  54. a_27_0, a nilpotent element of degree 27
  55. a_27_1, a nilpotent element of degree 27

About the group Ring generators Ring relations Completion information Restriction maps

Ring relations

There are 1414 minimal relations of maximal degree 54:

  1. a_5_02
  2. a_5_0·a_5_1
  3. a_5_0·a_5_2
  4. a_5_12
  5. a_5_1·a_5_2
  6. a_5_22
  7. a_6_0·a_5_0
  8. a_6_0·a_5_1
  9. a_6_0·a_5_2
  10. a_6_1·a_5_0
  11. a_6_1·a_5_1
  12. a_6_1·a_5_2
  13. a_6_2·a_5_0
  14. a_6_2·a_5_1
  15. a_6_2·a_5_2
  16. a_6_3·a_5_0
  17. a_6_3·a_5_1
  18. a_6_3·a_5_2
  19. a_6_02
  20. a_6_0·a_6_1
  21. a_6_0·a_6_2
  22. a_6_0·a_6_3
  23. a_6_12
  24. a_6_1·a_6_2
  25. a_6_1·a_6_3
  26. a_6_22
  27. a_6_2·a_6_3
  28. a_6_32
  29. a_5_0·a_7_0
  30. a_5_0·a_7_1
  31. a_5_1·a_7_0
  32. a_5_1·a_7_1
  33. a_5_2·a_7_0
  34. a_5_2·a_7_1
  35. a_6_0·a_7_0
  36. a_6_0·a_7_1
  37. a_6_1·a_7_0
  38. a_6_1·a_7_1
  39. a_6_2·a_7_0
  40. a_6_2·a_7_1
  41. a_6_3·a_7_0
  42. a_6_3·a_7_1
  43. a_8_0·a_5_0
  44. a_8_0·a_5_1
  45. a_8_0·a_5_2
  46. a_8_1·a_5_0
  47. a_8_1·a_5_1
  48. a_8_1·a_5_2
  49. a_8_2·a_5_0
  50. a_8_2·a_5_1
  51. a_8_2·a_5_2
  52. a_8_3·a_5_0
  53. a_8_3·a_5_1
  54. a_8_3·a_5_2
  55. a_6_0·a_8_1
  56. a_6_0·a_8_2
  57. a_6_0·a_8_3 + a_6_0·a_8_0
  58. a_6_1·a_8_0 + a_6_0·a_8_0
  59. a_6_1·a_8_1 + a_6_0·a_8_0
  60. a_6_1·a_8_2 + a_6_0·a_8_0
  61. a_6_1·a_8_3
  62. a_6_2·a_8_0
  63. a_6_2·a_8_1 + a_6_0·a_8_0
  64. a_6_2·a_8_2
  65. a_6_2·a_8_3
  66. a_6_3·a_8_0 + a_6_0·a_8_0
  67. a_6_3·a_8_1
  68. a_6_3·a_8_2
  69. a_6_3·a_8_3
  70. a_5_0·a_9_0
  71. a_5_0·a_9_1 + a_6_0·a_8_0
  72. a_5_0·a_9_2 + a_6_0·a_8_0
  73. a_5_1·a_9_0
  74. a_5_1·a_9_1 + a_6_0·a_8_0
  75. a_5_1·a_9_2
  76. a_5_2·a_9_0 + a_6_0·a_8_0
  77. a_5_2·a_9_1
  78. a_5_2·a_9_2
  79. a_7_02
  80. a_7_0·a_7_1 + a_6_0·a_8_0
  81. a_7_12
  82. a_6_0·a_9_0
  83. a_6_0·a_9_1
  84. a_6_0·a_9_2
  85. a_6_1·a_9_0
  86. a_6_1·a_9_1
  87. a_6_1·a_9_2
  88. a_6_2·a_9_0
  89. a_6_2·a_9_1
  90. a_6_2·a_9_2
  91. a_6_3·a_9_0
  92. a_6_3·a_9_1
  93. a_6_3·a_9_2
  94. a_8_0·a_7_0
  95. a_8_0·a_7_1
  96. a_8_1·a_7_0
  97. a_8_1·a_7_1
  98. a_8_2·a_7_0
  99. a_8_2·a_7_1
  100. a_8_3·a_7_0
  101. a_8_3·a_7_1
  102. a_8_02
  103. a_8_0·a_8_1
  104. a_8_0·a_8_2
  105. a_8_0·a_8_3
  106. a_8_12
  107. a_8_1·a_8_2
  108. a_8_1·a_8_3
  109. a_8_22
  110. a_8_2·a_8_3
  111. a_8_32
  112. a_5_0·a_11_0
  113. a_5_0·a_11_1
  114. a_5_1·a_11_0
  115. a_5_1·a_11_1
  116. a_5_2·a_11_0
  117. a_5_2·a_11_1
  118. a_7_0·a_9_0
  119. a_7_0·a_9_1
  120. a_7_0·a_9_2
  121. a_7_1·a_9_0
  122. a_7_1·a_9_1
  123. a_7_1·a_9_2
  124. a_6_0·a_11_0
  125. a_6_0·a_11_1
  126. a_6_1·a_11_0
  127. a_6_1·a_11_1
  128. a_6_2·a_11_0
  129. a_6_2·a_11_1
  130. a_6_3·a_11_0
  131. a_6_3·a_11_1
  132. a_8_0·a_9_0
  133. a_8_0·a_9_1
  134. a_8_0·a_9_2
  135. a_8_1·a_9_0
  136. a_8_1·a_9_1
  137. a_8_1·a_9_2
  138. a_8_2·a_9_0
  139. a_8_2·a_9_1
  140. a_8_2·a_9_2
  141. a_8_3·a_9_0
  142. a_8_3·a_9_1
  143. a_8_3·a_9_2
  144. a_12_0·a_5_0
  145. a_12_0·a_5_1
  146. a_12_0·a_5_2
  147. a_12_1·a_5_0
  148. a_12_1·a_5_1
  149. a_12_1·a_5_2
  150. a_12_2·a_5_0
  151. a_12_2·a_5_1
  152. a_12_2·a_5_2
  153. a_12_3·a_5_0
  154. a_12_3·a_5_1
  155. a_12_3·a_5_2
  156. a_6_0·a_12_0
  157. a_6_0·a_12_1
  158. a_6_0·a_12_2
  159. a_6_0·a_12_3
  160. a_6_1·a_12_0
  161. a_6_1·a_12_1
  162. a_6_1·a_12_2
  163. a_6_1·a_12_3
  164. a_6_2·a_12_0
  165. a_6_2·a_12_1
  166. a_6_2·a_12_2
  167. a_6_2·a_12_3
  168. a_6_3·a_12_0
  169. a_6_3·a_12_1
  170. a_6_3·a_12_2
  171. a_6_3·a_12_3
  172. a_5_0·a_13_0
  173. a_5_0·a_13_1
  174. a_5_1·a_13_0
  175. a_5_1·a_13_1
  176. a_5_2·a_13_0
  177. a_5_2·a_13_1
  178. a_7_0·a_11_0
  179. a_7_0·a_11_1
  180. a_7_1·a_11_0
  181. a_7_1·a_11_1
  182. a_9_02
  183. a_9_0·a_9_1
  184. a_9_0·a_9_2
  185. a_9_12
  186. a_9_1·a_9_2
  187. a_9_22
  188. a_6_0·a_13_0
  189. a_6_0·a_13_1
  190. a_6_1·a_13_0
  191. a_6_1·a_13_1
  192. a_6_2·a_13_0
  193. a_6_2·a_13_1
  194. a_6_3·a_13_0
  195. a_6_3·a_13_1
  196. a_8_0·a_11_0
  197. a_8_0·a_11_1
  198. a_8_1·a_11_0
  199. a_8_1·a_11_1
  200. a_8_2·a_11_0
  201. a_8_2·a_11_1
  202. a_8_3·a_11_0
  203. a_8_3·a_11_1
  204. a_12_0·a_7_0
  205. a_12_0·a_7_1
  206. a_12_1·a_7_0
  207. a_12_1·a_7_1
  208. a_12_2·a_7_0
  209. a_12_2·a_7_1
  210. a_12_3·a_7_0
  211. a_12_3·a_7_1
  212. a_8_0·a_12_0
  213. a_8_0·a_12_1
  214. a_8_0·a_12_2
  215. a_8_0·a_12_3
  216. a_8_1·a_12_0
  217. a_8_1·a_12_1
  218. a_8_1·a_12_2
  219. a_8_1·a_12_3
  220. a_8_2·a_12_0
  221. a_8_2·a_12_1
  222. a_8_2·a_12_2
  223. a_8_2·a_12_3
  224. a_8_3·a_12_0
  225. a_8_3·a_12_1
  226. a_8_3·a_12_2
  227. a_8_3·a_12_3
  228. a_5_0·a_15_0
  229. a_5_0·a_15_1
  230. a_5_1·a_15_0
  231. a_5_1·a_15_1
  232. a_5_2·a_15_0
  233. a_5_2·a_15_1
  234. a_7_0·a_13_0
  235. a_7_0·a_13_1
  236. a_7_1·a_13_0
  237. a_7_1·a_13_1
  238. a_9_0·a_11_0
  239. a_9_0·a_11_1
  240. a_9_1·a_11_0
  241. a_9_1·a_11_1
  242. a_9_2·a_11_0
  243. a_9_2·a_11_1
  244. a_6_0·a_15_0
  245. a_6_0·a_15_1
  246. a_6_1·a_15_0
  247. a_6_1·a_15_1
  248. a_6_2·a_15_0
  249. a_6_2·a_15_1
  250. a_6_3·a_15_0
  251. a_6_3·a_15_1
  252. a_8_0·a_13_0
  253. a_8_0·a_13_1
  254. a_8_1·a_13_0
  255. a_8_1·a_13_1
  256. a_8_2·a_13_0
  257. a_8_2·a_13_1
  258. a_8_3·a_13_0
  259. a_8_3·a_13_1
  260. a_12_0·a_9_0
  261. a_12_0·a_9_1
  262. a_12_0·a_9_2
  263. a_12_1·a_9_0
  264. a_12_1·a_9_1
  265. a_12_1·a_9_2
  266. a_12_2·a_9_0
  267. a_12_2·a_9_1
  268. a_12_2·a_9_2
  269. a_12_3·a_9_0
  270. a_12_3·a_9_1
  271. a_12_3·a_9_2
  272. a_5_0·a_17_0
  273. a_5_0·a_17_1
  274. a_5_1·a_17_0
  275. a_5_1·a_17_1
  276. a_5_2·a_17_0
  277. a_5_2·a_17_1
  278. a_7_0·a_15_0
  279. a_7_0·a_15_1
  280. a_7_1·a_15_0
  281. a_7_1·a_15_1
  282. a_9_0·a_13_0
  283. a_9_0·a_13_1
  284. a_9_1·a_13_0
  285. a_9_1·a_13_1
  286. a_9_2·a_13_0
  287. a_9_2·a_13_1
  288. a_11_02
  289. a_11_0·a_11_1
  290. a_11_12
  291. a_6_0·a_17_0
  292. a_6_0·a_17_1
  293. a_6_1·a_17_0
  294. a_6_1·a_17_1
  295. a_6_2·a_17_0
  296. a_6_2·a_17_1
  297. a_6_3·a_17_0
  298. a_6_3·a_17_1
  299. a_8_0·a_15_0
  300. a_8_0·a_15_1
  301. a_8_1·a_15_0
  302. a_8_1·a_15_1
  303. a_8_2·a_15_0
  304. a_8_2·a_15_1
  305. a_8_3·a_15_0
  306. a_8_3·a_15_1
  307. a_12_0·a_11_0
  308. a_12_0·a_11_1
  309. a_12_1·a_11_0
  310. a_12_1·a_11_1
  311. a_12_2·a_11_0
  312. a_12_2·a_11_1
  313. a_12_3·a_11_0
  314. a_12_3·a_11_1
  315. a_18_0·a_5_0
  316. a_18_0·a_5_1
  317. a_18_0·a_5_2
  318. a_18_1·a_5_0
  319. a_18_1·a_5_1
  320. a_18_1·a_5_2
  321. a_18_2·a_5_0
  322. a_18_2·a_5_1
  323. a_18_2·a_5_2
  324. a_18_3·a_5_0
  325. a_18_3·a_5_1
  326. a_18_3·a_5_2
  327. a_6_0·a_18_0
  328. a_6_0·a_18_1
  329. a_6_0·a_18_2
  330. a_6_0·a_18_3
  331. a_6_1·a_18_0
  332. a_6_1·a_18_1
  333. a_6_1·a_18_2
  334. a_6_1·a_18_3
  335. a_6_2·a_18_0
  336. a_6_2·a_18_1
  337. a_6_2·a_18_2
  338. a_6_2·a_18_3
  339. a_6_3·a_18_0
  340. a_6_3·a_18_1
  341. a_6_3·a_18_2
  342. a_6_3·a_18_3
  343. a_12_02
  344. a_12_0·a_12_1
  345. a_12_0·a_12_2
  346. a_12_0·a_12_3
  347. a_12_12
  348. a_12_1·a_12_2
  349. a_12_1·a_12_3
  350. a_12_22
  351. a_12_2·a_12_3
  352. a_12_32
  353. a_5_0·a_19_0
  354. a_5_0·a_19_1
  355. a_5_0·a_19_2
  356. a_5_0·a_19_3
  357. a_5_1·a_19_0
  358. a_5_1·a_19_1
  359. a_5_1·a_19_2
  360. a_5_1·a_19_3
  361. a_5_2·a_19_0
  362. a_5_2·a_19_1
  363. a_5_2·a_19_2
  364. a_5_2·a_19_3
  365. a_7_0·a_17_0
  366. a_7_0·a_17_1
  367. a_7_1·a_17_0
  368. a_7_1·a_17_1
  369. a_9_0·a_15_0
  370. a_9_0·a_15_1
  371. a_9_1·a_15_0
  372. a_9_1·a_15_1
  373. a_9_2·a_15_0
  374. a_9_2·a_15_1
  375. a_11_0·a_13_0
  376. a_11_0·a_13_1
  377. a_11_1·a_13_0
  378. a_11_1·a_13_1
  379. a_6_0·a_19_0
  380. a_6_0·a_19_1
  381. a_6_0·a_19_2
  382. a_6_0·a_19_3
  383. a_6_1·a_19_0
  384. a_6_1·a_19_1
  385. a_6_1·a_19_2
  386. a_6_1·a_19_3
  387. a_6_2·a_19_0
  388. a_6_2·a_19_1
  389. a_6_2·a_19_2
  390. a_6_2·a_19_3
  391. a_6_3·a_19_0
  392. a_6_3·a_19_1
  393. a_6_3·a_19_2
  394. a_6_3·a_19_3
  395. a_8_0·a_17_0
  396. a_8_0·a_17_1
  397. a_8_1·a_17_0
  398. a_8_1·a_17_1
  399. a_8_2·a_17_0
  400. a_8_2·a_17_1
  401. a_8_3·a_17_0
  402. a_8_3·a_17_1
  403. a_12_0·a_13_0
  404. a_12_0·a_13_1
  405. a_12_1·a_13_0
  406. a_12_1·a_13_1
  407. a_12_2·a_13_0
  408. a_12_2·a_13_1
  409. a_12_3·a_13_0
  410. a_12_3·a_13_1
  411. a_18_0·a_7_0
  412. a_18_0·a_7_1
  413. a_18_1·a_7_0
  414. a_18_1·a_7_1
  415. a_18_2·a_7_0
  416. a_18_2·a_7_1
  417. a_18_3·a_7_0
  418. a_18_3·a_7_1
  419. a_20_0·a_5_0
  420. a_20_0·a_5_1
  421. a_20_0·a_5_2
  422. a_20_1·a_5_0
  423. a_20_1·a_5_1
  424. a_20_1·a_5_2
  425. a_20_2·a_5_0
  426. a_20_2·a_5_1
  427. a_20_2·a_5_2
  428. a_20_3·a_5_0
  429. a_20_3·a_5_1
  430. a_20_3·a_5_2
  431. a_6_0·a_20_0
  432. a_6_0·a_20_1
  433. a_6_0·a_20_2
  434. a_6_0·a_20_3
  435. a_6_1·a_20_0
  436. a_6_1·a_20_1
  437. a_6_1·a_20_2
  438. a_6_1·a_20_3
  439. a_6_2·a_20_0
  440. a_6_2·a_20_1
  441. a_6_2·a_20_2
  442. a_6_2·a_20_3
  443. a_6_3·a_20_0
  444. a_6_3·a_20_1
  445. a_6_3·a_20_2
  446. a_6_3·a_20_3
  447. a_8_0·a_18_0
  448. a_8_0·a_18_1
  449. a_8_0·a_18_2
  450. a_8_0·a_18_3
  451. a_8_1·a_18_0
  452. a_8_1·a_18_1
  453. a_8_1·a_18_2
  454. a_8_1·a_18_3
  455. a_8_2·a_18_0
  456. a_8_2·a_18_1
  457. a_8_2·a_18_2
  458. a_8_2·a_18_3
  459. a_8_3·a_18_0
  460. a_8_3·a_18_1
  461. a_8_3·a_18_2
  462. a_8_3·a_18_3
  463. a_5_0·a_21_3
  464. a_5_0·a_21_4
  465. a_5_1·a_21_3
  466. a_5_1·a_21_4
  467. a_5_2·a_21_3
  468. a_5_2·a_21_4
  469. a_7_0·a_19_0
  470. a_7_0·a_19_1
  471. a_7_0·a_19_2
  472. a_7_0·a_19_3
  473. a_7_1·a_19_0
  474. a_7_1·a_19_1
  475. a_7_1·a_19_2
  476. a_7_1·a_19_3
  477. a_9_0·a_17_0
  478. a_9_0·a_17_1
  479. a_9_1·a_17_0
  480. a_9_1·a_17_1
  481. a_9_2·a_17_0
  482. a_9_2·a_17_1
  483. a_11_0·a_15_0
  484. a_11_0·a_15_1
  485. a_11_1·a_15_0
  486. a_11_1·a_15_1
  487. a_13_02
  488. a_13_0·a_13_1
  489. a_13_12
  490. a_6_0·a_21_3
  491. a_6_0·a_21_4
  492. a_6_1·a_21_3
  493. a_6_1·a_21_4
  494. a_6_2·a_21_3
  495. a_6_2·a_21_4
  496. a_6_3·a_21_3
  497. a_6_3·a_21_4
  498. a_8_0·a_19_0
  499. a_8_0·a_19_1
  500. a_8_0·a_19_2
  501. a_8_0·a_19_3
  502. a_8_1·a_19_0
  503. a_8_1·a_19_1
  504. a_8_1·a_19_2
  505. a_8_1·a_19_3
  506. a_8_2·a_19_0
  507. a_8_2·a_19_1
  508. a_8_2·a_19_2
  509. a_8_2·a_19_3
  510. a_8_3·a_19_0
  511. a_8_3·a_19_1
  512. a_8_3·a_19_2
  513. a_8_3·a_19_3
  514. a_12_0·a_15_0
  515. a_12_0·a_15_1
  516. a_12_1·a_15_0
  517. a_12_1·a_15_1
  518. a_12_2·a_15_0
  519. a_12_2·a_15_1
  520. a_12_3·a_15_0
  521. a_12_3·a_15_1
  522. a_18_0·a_9_0
  523. a_18_0·a_9_1
  524. a_18_0·a_9_2
  525. a_18_1·a_9_0
  526. a_18_1·a_9_1
  527. a_18_1·a_9_2
  528. a_18_2·a_9_0
  529. a_18_2·a_9_1
  530. a_18_2·a_9_2
  531. a_18_3·a_9_0
  532. a_18_3·a_9_1
  533. a_18_3·a_9_2
  534. a_20_0·a_7_0
  535. a_20_0·a_7_1
  536. a_20_1·a_7_0
  537. a_20_1·a_7_1
  538. a_20_2·a_7_0
  539. a_20_2·a_7_1
  540. a_20_3·a_7_0
  541. a_20_3·a_7_1
  542. a_8_0·a_20_0
  543. a_8_0·a_20_1
  544. a_8_0·a_20_2
  545. a_8_0·a_20_3
  546. a_8_1·a_20_0
  547. a_8_1·a_20_1
  548. a_8_1·a_20_2
  549. a_8_1·a_20_3
  550. a_8_2·a_20_0
  551. a_8_2·a_20_1
  552. a_8_2·a_20_2
  553. a_8_2·a_20_3
  554. a_8_3·a_20_0
  555. a_8_3·a_20_1
  556. a_8_3·a_20_2
  557. a_8_3·a_20_3
  558. a_5_0·a_23_2
  559. a_5_0·a_23_3
  560. a_5_1·a_23_2
  561. a_5_1·a_23_3
  562. a_5_2·a_23_2
  563. a_5_2·a_23_3
  564. a_7_0·a_21_3
  565. a_7_0·a_21_4
  566. a_7_1·a_21_3
  567. a_7_1·a_21_4
  568. a_9_0·a_19_0
  569. a_9_0·a_19_1
  570. a_9_0·a_19_2
  571. a_9_0·a_19_3
  572. a_9_1·a_19_0
  573. a_9_1·a_19_1
  574. a_9_1·a_19_2
  575. a_9_1·a_19_3
  576. a_9_2·a_19_0
  577. a_9_2·a_19_1
  578. a_9_2·a_19_2
  579. a_9_2·a_19_3
  580. a_11_0·a_17_0
  581. a_11_0·a_17_1
  582. a_11_1·a_17_0
  583. a_11_1·a_17_1
  584. a_13_0·a_15_0
  585. a_13_0·a_15_1
  586. a_13_1·a_15_0
  587. a_13_1·a_15_1
  588. a_6_0·a_23_2
  589. a_6_0·a_23_3
  590. a_6_1·a_23_2
  591. a_6_1·a_23_3
  592. a_6_2·a_23_2
  593. a_6_2·a_23_3
  594. a_6_3·a_23_2
  595. a_6_3·a_23_3
  596. a_8_0·a_21_3
  597. a_8_0·a_21_4
  598. a_8_1·a_21_3
  599. a_8_1·a_21_4
  600. a_8_2·a_21_3
  601. a_8_2·a_21_4
  602. a_8_3·a_21_3
  603. a_8_3·a_21_4
  604. a_12_0·a_17_0
  605. a_12_0·a_17_1
  606. a_12_1·a_17_0
  607. a_12_1·a_17_1
  608. a_12_2·a_17_0
  609. a_12_2·a_17_1
  610. a_12_3·a_17_0
  611. a_12_3·a_17_1
  612. a_18_0·a_11_0
  613. a_18_0·a_11_1
  614. a_18_1·a_11_0
  615. a_18_1·a_11_1
  616. a_18_2·a_11_0
  617. a_18_2·a_11_1
  618. a_18_3·a_11_0
  619. a_18_3·a_11_1
  620. a_20_0·a_9_0
  621. a_20_0·a_9_1
  622. a_20_0·a_9_2
  623. a_20_1·a_9_0
  624. a_20_1·a_9_1
  625. a_20_1·a_9_2
  626. a_20_2·a_9_0
  627. a_20_2·a_9_1
  628. a_20_2·a_9_2
  629. a_20_3·a_9_0
  630. a_20_3·a_9_1
  631. a_20_3·a_9_2
  632. a_12_0·a_18_0
  633. a_12_0·a_18_1
  634. a_12_0·a_18_2
  635. a_12_0·a_18_3 + a_6_0·a_8_0·c_16_0
  636. a_12_1·a_18_0
  637. a_12_1·a_18_1
  638. a_12_1·a_18_2 + a_6_0·a_8_0·c_16_0
  639. a_12_1·a_18_3
  640. a_12_2·a_18_0
  641. a_12_2·a_18_1 + a_6_0·a_8_0·c_16_0
  642. a_12_2·a_18_2
  643. a_12_2·a_18_3
  644. a_12_3·a_18_0 + a_6_0·a_8_0·c_16_0
  645. a_12_3·a_18_1
  646. a_12_3·a_18_2
  647. a_12_3·a_18_3
  648. a_5_0·a_25_0
  649. a_5_0·a_25_1 + a_6_0·a_8_0·c_16_0
  650. a_5_1·a_25_0
  651. a_5_1·a_25_1
  652. a_5_2·a_25_0 + a_6_0·a_8_0·c_16_0
  653. a_5_2·a_25_1
  654. a_7_0·a_23_2
  655. a_7_0·a_23_3 + a_6_0·a_8_0·c_16_0
  656. a_7_1·a_23_2 + a_6_0·a_8_0·c_16_0
  657. a_7_1·a_23_3
  658. a_9_0·a_21_3
  659. a_9_0·a_21_4
  660. a_9_1·a_21_3
  661. a_9_1·a_21_4
  662. a_9_2·a_21_3
  663. a_9_2·a_21_4
  664. a_11_0·a_19_0 + a_6_0·a_8_0·c_16_0
  665. a_11_0·a_19_1 + a_6_0·a_8_0·c_16_0
  666. a_11_0·a_19_2
  667. a_11_0·a_19_3
  668. a_11_1·a_19_0 + a_6_0·a_8_0·c_16_0
  669. a_11_1·a_19_1
  670. a_11_1·a_19_2
  671. a_11_1·a_19_3
  672. a_13_0·a_17_0
  673. a_13_0·a_17_1 + a_6_0·a_8_0·c_16_0
  674. a_13_1·a_17_0 + a_6_0·a_8_0·c_16_0
  675. a_13_1·a_17_1
  676. a_15_02
  677. a_15_0·a_15_1 + a_6_0·a_8_0·c_16_0
  678. a_15_12
  679. a_6_0·a_25_0
  680. a_6_0·a_25_1
  681. a_6_1·a_25_0
  682. a_6_1·a_25_1
  683. a_6_2·a_25_0
  684. a_6_2·a_25_1
  685. a_6_3·a_25_0
  686. a_6_3·a_25_1
  687. a_8_0·a_23_2
  688. a_8_0·a_23_3
  689. a_8_1·a_23_2
  690. a_8_1·a_23_3
  691. a_8_2·a_23_2
  692. a_8_2·a_23_3
  693. a_8_3·a_23_2
  694. a_8_3·a_23_3
  695. a_12_0·a_19_0
  696. a_12_0·a_19_1
  697. a_12_0·a_19_2
  698. a_12_0·a_19_3
  699. a_12_1·a_19_0
  700. a_12_1·a_19_1
  701. a_12_1·a_19_2
  702. a_12_1·a_19_3
  703. a_12_2·a_19_0
  704. a_12_2·a_19_1
  705. a_12_2·a_19_2
  706. a_12_2·a_19_3
  707. a_12_3·a_19_0
  708. a_12_3·a_19_1
  709. a_12_3·a_19_2
  710. a_12_3·a_19_3
  711. a_18_0·a_13_0
  712. a_18_0·a_13_1
  713. a_18_1·a_13_0
  714. a_18_1·a_13_1
  715. a_18_2·a_13_0
  716. a_18_2·a_13_1
  717. a_18_3·a_13_0
  718. a_18_3·a_13_1
  719. a_20_0·a_11_0
  720. a_20_0·a_11_1
  721. a_20_1·a_11_0
  722. a_20_1·a_11_1
  723. a_20_2·a_11_0
  724. a_20_2·a_11_1
  725. a_20_3·a_11_0
  726. a_20_3·a_11_1
  727. a_26_0·a_5_0
  728. a_26_0·a_5_1
  729. a_26_0·a_5_2
  730. a_26_1·a_5_0
  731. a_26_1·a_5_1
  732. a_26_1·a_5_2
  733. a_26_2·a_5_0
  734. a_26_2·a_5_1
  735. a_26_2·a_5_2
  736. a_26_3·a_5_0
  737. a_26_3·a_5_1
  738. a_26_3·a_5_2
  739. a_6_0·a_26_0
  740. a_6_0·a_26_1
  741. a_6_0·a_26_2
  742. a_6_0·a_26_3
  743. a_6_1·a_26_0
  744. a_6_1·a_26_1
  745. a_6_1·a_26_2
  746. a_6_1·a_26_3
  747. a_6_2·a_26_0
  748. a_6_2·a_26_1
  749. a_6_2·a_26_2
  750. a_6_2·a_26_3
  751. a_6_3·a_26_0
  752. a_6_3·a_26_1
  753. a_6_3·a_26_2
  754. a_6_3·a_26_3
  755. a_12_0·a_20_0
  756. a_12_0·a_20_1
  757. a_12_0·a_20_2
  758. a_12_0·a_20_3
  759. a_12_1·a_20_0
  760. a_12_1·a_20_1
  761. a_12_1·a_20_2
  762. a_12_1·a_20_3
  763. a_12_2·a_20_0
  764. a_12_2·a_20_1
  765. a_12_2·a_20_2
  766. a_12_2·a_20_3
  767. a_12_3·a_20_0
  768. a_12_3·a_20_1
  769. a_12_3·a_20_2
  770. a_12_3·a_20_3
  771. a_5_0·a_27_0
  772. a_5_0·a_27_1
  773. a_5_1·a_27_0
  774. a_5_1·a_27_1
  775. a_5_2·a_27_0
  776. a_5_2·a_27_1
  777. a_7_0·a_25_0
  778. a_7_0·a_25_1
  779. a_7_1·a_25_0
  780. a_7_1·a_25_1
  781. a_9_0·a_23_2
  782. a_9_0·a_23_3
  783. a_9_1·a_23_2
  784. a_9_1·a_23_3
  785. a_9_2·a_23_2
  786. a_9_2·a_23_3
  787. a_11_0·a_21_3
  788. a_11_0·a_21_4
  789. a_11_1·a_21_3
  790. a_11_1·a_21_4
  791. a_13_0·a_19_0
  792. a_13_0·a_19_1
  793. a_13_0·a_19_2
  794. a_13_0·a_19_3
  795. a_13_1·a_19_0
  796. a_13_1·a_19_1
  797. a_13_1·a_19_2
  798. a_13_1·a_19_3
  799. a_15_0·a_17_0
  800. a_15_0·a_17_1
  801. a_15_1·a_17_0
  802. a_15_1·a_17_1
  803. a_6_0·a_27_0
  804. a_6_0·a_27_1
  805. a_6_1·a_27_0
  806. a_6_1·a_27_1
  807. a_6_2·a_27_0
  808. a_6_2·a_27_1
  809. a_6_3·a_27_0
  810. a_6_3·a_27_1
  811. a_8_0·a_25_0
  812. a_8_0·a_25_1
  813. a_8_1·a_25_0
  814. a_8_1·a_25_1
  815. a_8_2·a_25_0
  816. a_8_2·a_25_1
  817. a_8_3·a_25_0
  818. a_8_3·a_25_1
  819. a_12_0·a_21_3
  820. a_12_0·a_21_4
  821. a_12_1·a_21_3
  822. a_12_1·a_21_4
  823. a_12_2·a_21_3
  824. a_12_2·a_21_4
  825. a_12_3·a_21_3
  826. a_12_3·a_21_4
  827. a_18_0·a_15_0
  828. a_18_0·a_15_1
  829. a_18_1·a_15_0
  830. a_18_1·a_15_1
  831. a_18_2·a_15_0
  832. a_18_2·a_15_1
  833. a_18_3·a_15_0
  834. a_18_3·a_15_1
  835. a_20_0·a_13_0
  836. a_20_0·a_13_1
  837. a_20_1·a_13_0
  838. a_20_1·a_13_1
  839. a_20_2·a_13_0
  840. a_20_2·a_13_1
  841. a_20_3·a_13_0
  842. a_20_3·a_13_1
  843. a_26_0·a_7_0
  844. a_26_0·a_7_1
  845. a_26_1·a_7_0
  846. a_26_1·a_7_1
  847. a_26_2·a_7_0
  848. a_26_2·a_7_1
  849. a_26_3·a_7_0
  850. a_26_3·a_7_1
  851. a_8_0·a_26_0
  852. a_8_0·a_26_1
  853. a_8_0·a_26_2
  854. a_8_0·a_26_3
  855. a_8_1·a_26_0
  856. a_8_1·a_26_1
  857. a_8_1·a_26_2
  858. a_8_1·a_26_3
  859. a_8_2·a_26_0
  860. a_8_2·a_26_1
  861. a_8_2·a_26_2
  862. a_8_2·a_26_3
  863. a_8_3·a_26_0
  864. a_8_3·a_26_1
  865. a_8_3·a_26_2
  866. a_8_3·a_26_3
  867. a_7_0·a_27_0
  868. a_7_0·a_27_1
  869. a_7_1·a_27_0
  870. a_7_1·a_27_1
  871. a_9_0·a_25_0
  872. a_9_0·a_25_1
  873. a_9_1·a_25_0
  874. a_9_1·a_25_1
  875. a_9_2·a_25_0
  876. a_9_2·a_25_1
  877. a_11_0·a_23_2
  878. a_11_0·a_23_3
  879. a_11_1·a_23_2
  880. a_11_1·a_23_3
  881. a_13_0·a_21_3
  882. a_13_0·a_21_4
  883. a_13_1·a_21_3
  884. a_13_1·a_21_4
  885. a_15_0·a_19_0
  886. a_15_0·a_19_1
  887. a_15_0·a_19_2
  888. a_15_0·a_19_3
  889. a_15_1·a_19_0
  890. a_15_1·a_19_1
  891. a_15_1·a_19_2
  892. a_15_1·a_19_3
  893. a_17_02
  894. a_17_0·a_17_1
  895. a_17_12
  896. c_24_5·a_11_0 + c_24_4·a_11_1 + c_16_0·a_19_3 + c_16_0·a_19_2
  897. c_24_5·a_11_1 + c_24_4·a_11_1 + c_24_4·a_11_0 + c_16_0·a_19_2
  898. a_8_0·a_27_0
  899. a_8_0·a_27_1
  900. a_8_1·a_27_0
  901. a_8_1·a_27_1
  902. a_8_2·a_27_0
  903. a_8_2·a_27_1
  904. a_8_3·a_27_0
  905. a_8_3·a_27_1
  906. a_12_0·a_23_2
  907. a_12_0·a_23_3
  908. a_12_1·a_23_2
  909. a_12_1·a_23_3
  910. a_12_2·a_23_2
  911. a_12_2·a_23_3
  912. a_12_3·a_23_2
  913. a_12_3·a_23_3
  914. a_18_0·a_17_0
  915. a_18_0·a_17_1
  916. a_18_1·a_17_0
  917. a_18_1·a_17_1
  918. a_18_2·a_17_0
  919. a_18_2·a_17_1
  920. a_18_3·a_17_0
  921. a_18_3·a_17_1
  922. a_20_0·a_15_0
  923. a_20_0·a_15_1
  924. a_20_1·a_15_0
  925. a_20_1·a_15_1
  926. a_20_2·a_15_0
  927. a_20_2·a_15_1
  928. a_20_3·a_15_0
  929. a_20_3·a_15_1
  930. a_26_0·a_9_0
  931. a_26_0·a_9_1
  932. a_26_0·a_9_2
  933. a_26_1·a_9_0
  934. a_26_1·a_9_1
  935. a_26_1·a_9_2
  936. a_26_2·a_9_0
  937. a_26_2·a_9_1
  938. a_26_2·a_9_2
  939. a_26_3·a_9_0
  940. a_26_3·a_9_1
  941. a_26_3·a_9_2
  942. c_16_0·a_20_0 + a_12_1·c_24_5 + a_12_1·c_24_4 + a_12_0·c_24_4
  943. c_16_0·a_20_1 + a_12_1·c_24_5 + a_12_0·c_24_5 + a_12_0·c_24_4
  944. c_16_0·a_20_2 + a_12_3·c_24_5 + a_12_3·c_24_4 + a_12_2·c_24_4
  945. c_16_0·a_20_3 + a_12_3·c_24_5 + a_12_2·c_24_5 + a_12_2·c_24_4
  946. a_18_02
  947. a_18_0·a_18_1
  948. a_18_0·a_18_2
  949. a_18_0·a_18_3
  950. a_18_12
  951. a_18_1·a_18_2
  952. a_18_1·a_18_3
  953. a_18_22
  954. a_18_2·a_18_3
  955. a_18_32
  956. a_9_0·a_27_0
  957. a_9_0·a_27_1
  958. a_9_1·a_27_0
  959. a_9_1·a_27_1
  960. a_9_2·a_27_0
  961. a_9_2·a_27_1
  962. a_11_0·a_25_0
  963. a_11_0·a_25_1
  964. a_11_1·a_25_0
  965. a_11_1·a_25_1
  966. a_13_0·a_23_2
  967. a_13_0·a_23_3
  968. a_13_1·a_23_2
  969. a_13_1·a_23_3
  970. a_15_0·a_21_3
  971. a_15_0·a_21_4
  972. a_15_1·a_21_3
  973. a_15_1·a_21_4
  974. a_17_0·a_19_0
  975. a_17_0·a_19_1
  976. a_17_0·a_19_2
  977. a_17_0·a_19_3
  978. a_17_1·a_19_0
  979. a_17_1·a_19_1
  980. a_17_1·a_19_2
  981. a_17_1·a_19_3
  982. c_24_5·a_13_0 + c_24_4·a_13_1 + c_24_4·a_13_0 + c_16_0·a_21_4
  983. c_24_5·a_13_1 + c_24_4·a_13_0 + c_16_0·a_21_4 + c_16_0·a_21_3
  984. a_12_0·a_25_0
  985. a_12_0·a_25_1
  986. a_12_1·a_25_0
  987. a_12_1·a_25_1
  988. a_12_2·a_25_0
  989. a_12_2·a_25_1
  990. a_12_3·a_25_0
  991. a_12_3·a_25_1
  992. a_18_0·a_19_0
  993. a_18_0·a_19_1
  994. a_18_0·a_19_2
  995. a_18_0·a_19_3
  996. a_18_1·a_19_0
  997. a_18_1·a_19_1
  998. a_18_1·a_19_2
  999. a_18_1·a_19_3
  1000. a_18_2·a_19_0
  1001. a_18_2·a_19_1
  1002. a_18_2·a_19_2
  1003. a_18_2·a_19_3
  1004. a_18_3·a_19_0
  1005. a_18_3·a_19_1
  1006. a_18_3·a_19_2
  1007. a_18_3·a_19_3
  1008. a_20_0·a_17_0
  1009. a_20_0·a_17_1
  1010. a_20_1·a_17_0
  1011. a_20_1·a_17_1
  1012. a_20_2·a_17_0
  1013. a_20_2·a_17_1
  1014. a_20_3·a_17_0
  1015. a_20_3·a_17_1
  1016. a_26_0·a_11_0
  1017. a_26_0·a_11_1
  1018. a_26_1·a_11_0
  1019. a_26_1·a_11_1
  1020. a_26_2·a_11_0
  1021. a_26_2·a_11_1
  1022. a_26_3·a_11_0
  1023. a_26_3·a_11_1
  1024. a_12_0·a_26_0
  1025. a_12_0·a_26_1
  1026. a_12_0·a_26_2 + a_6_0·a_8_0·c_24_5 + a_6_0·a_8_0·c_24_4
  1027. a_12_0·a_26_3 + a_6_0·a_8_0·c_24_5
  1028. a_12_1·a_26_0
  1029. a_12_1·a_26_1
  1030. a_12_1·a_26_2 + a_6_0·a_8_0·c_24_4
  1031. a_12_1·a_26_3 + a_6_0·a_8_0·c_24_5 + a_6_0·a_8_0·c_24_4
  1032. a_12_2·a_26_0 + a_6_0·a_8_0·c_24_5 + a_6_0·a_8_0·c_24_4
  1033. a_12_2·a_26_1 + a_6_0·a_8_0·c_24_5
  1034. a_12_2·a_26_2
  1035. a_12_2·a_26_3
  1036. a_12_3·a_26_0 + a_6_0·a_8_0·c_24_4
  1037. a_12_3·a_26_1 + a_6_0·a_8_0·c_24_5 + a_6_0·a_8_0·c_24_4
  1038. a_12_3·a_26_2
  1039. a_12_3·a_26_3
  1040. a_18_0·a_20_0
  1041. a_18_0·a_20_1
  1042. a_18_0·a_20_2 + a_6_0·a_8_0·c_24_5 + a_6_0·a_8_0·c_24_4
  1043. a_18_0·a_20_3 + a_6_0·a_8_0·c_24_5
  1044. a_18_1·a_20_0
  1045. a_18_1·a_20_1
  1046. a_18_1·a_20_2 + a_6_0·a_8_0·c_24_4
  1047. a_18_1·a_20_3 + a_6_0·a_8_0·c_24_5 + a_6_0·a_8_0·c_24_4
  1048. a_18_2·a_20_0 + a_6_0·a_8_0·c_24_5 + a_6_0·a_8_0·c_24_4
  1049. a_18_2·a_20_1 + a_6_0·a_8_0·c_24_5
  1050. a_18_2·a_20_2
  1051. a_18_2·a_20_3
  1052. a_18_3·a_20_0 + a_6_0·a_8_0·c_24_4
  1053. a_18_3·a_20_1 + a_6_0·a_8_0·c_24_5 + a_6_0·a_8_0·c_24_4
  1054. a_18_3·a_20_2
  1055. a_18_3·a_20_3
  1056. a_11_0·a_27_0 + a_6_0·a_8_0·c_24_4
  1057. a_11_0·a_27_1 + a_6_0·a_8_0·c_24_5
  1058. a_11_1·a_27_0 + a_6_0·a_8_0·c_24_5
  1059. a_11_1·a_27_1 + a_6_0·a_8_0·c_24_5 + a_6_0·a_8_0·c_24_4
  1060. a_13_0·a_25_0 + a_6_0·a_8_0·c_24_5 + a_6_0·a_8_0·c_24_4
  1061. a_13_0·a_25_1 + a_6_0·a_8_0·c_24_4
  1062. a_13_1·a_25_0 + a_6_0·a_8_0·c_24_5
  1063. a_13_1·a_25_1 + a_6_0·a_8_0·c_24_5 + a_6_0·a_8_0·c_24_4
  1064. a_15_0·a_23_2 + a_6_0·a_8_0·c_24_5 + a_6_0·a_8_0·c_24_4
  1065. a_15_0·a_23_3 + a_6_0·a_8_0·c_24_4
  1066. a_15_1·a_23_2 + a_6_0·a_8_0·c_24_5
  1067. a_15_1·a_23_3 + a_6_0·a_8_0·c_24_5 + a_6_0·a_8_0·c_24_4
  1068. a_17_0·a_21_3 + a_6_0·a_8_0·c_24_5 + a_6_0·a_8_0·c_24_4
  1069. a_17_0·a_21_4 + a_6_0·a_8_0·c_24_4
  1070. a_17_1·a_21_3 + a_6_0·a_8_0·c_24_5
  1071. a_17_1·a_21_4 + a_6_0·a_8_0·c_24_5 + a_6_0·a_8_0·c_24_4
  1072. a_19_02
  1073. a_19_0·a_19_1 + a_6_0·a_8_0·c_24_4
  1074. a_19_0·a_19_2 + a_6_0·a_8_0·c_24_5
  1075. a_19_0·a_19_3 + a_6_0·a_8_0·c_24_4
  1076. a_19_12
  1077. a_19_1·a_19_2 + a_6_0·a_8_0·c_24_4
  1078. a_19_1·a_19_3 + a_6_0·a_8_0·c_24_5 + a_6_0·a_8_0·c_24_4
  1079. a_19_22
  1080. a_19_2·a_19_3
  1081. a_19_32
  1082. c_24_5·a_15_0 + c_24_4·a_15_1 + c_24_4·a_15_0 + c_16_0·a_23_3 + c_16_02·a_7_1
  1083. c_24_5·a_15_1 + c_24_4·a_15_0 + c_16_0·a_23_3 + c_16_0·a_23_2 + c_16_02·a_7_1
       + c_16_02·a_7_0
  1084. a_12_0·a_27_0
  1085. a_12_0·a_27_1
  1086. a_12_1·a_27_0
  1087. a_12_1·a_27_1
  1088. a_12_2·a_27_0
  1089. a_12_2·a_27_1
  1090. a_12_3·a_27_0
  1091. a_12_3·a_27_1
  1092. a_18_0·a_21_3
  1093. a_18_0·a_21_4
  1094. a_18_1·a_21_3
  1095. a_18_1·a_21_4
  1096. a_18_2·a_21_3
  1097. a_18_2·a_21_4
  1098. a_18_3·a_21_3
  1099. a_18_3·a_21_4
  1100. a_20_0·a_19_0
  1101. a_20_0·a_19_1
  1102. a_20_0·a_19_2
  1103. a_20_0·a_19_3
  1104. a_20_1·a_19_0
  1105. a_20_1·a_19_1
  1106. a_20_1·a_19_2
  1107. a_20_1·a_19_3
  1108. a_20_2·a_19_0
  1109. a_20_2·a_19_1
  1110. a_20_2·a_19_2
  1111. a_20_2·a_19_3
  1112. a_20_3·a_19_0
  1113. a_20_3·a_19_1
  1114. a_20_3·a_19_2
  1115. a_20_3·a_19_3
  1116. a_26_0·a_13_0
  1117. a_26_0·a_13_1
  1118. a_26_1·a_13_0
  1119. a_26_1·a_13_1
  1120. a_26_2·a_13_0
  1121. a_26_2·a_13_1
  1122. a_26_3·a_13_0
  1123. a_26_3·a_13_1
  1124. a_20_02
  1125. a_20_0·a_20_1
  1126. a_20_0·a_20_2
  1127. a_20_0·a_20_3
  1128. a_20_12
  1129. a_20_1·a_20_2
  1130. a_20_1·a_20_3
  1131. a_20_22
  1132. a_20_2·a_20_3
  1133. a_20_32
  1134. a_13_0·a_27_0
  1135. a_13_0·a_27_1
  1136. a_13_1·a_27_0
  1137. a_13_1·a_27_1
  1138. a_15_0·a_25_0
  1139. a_15_0·a_25_1
  1140. a_15_1·a_25_0
  1141. a_15_1·a_25_1
  1142. a_17_0·a_23_2
  1143. a_17_0·a_23_3
  1144. a_17_1·a_23_2
  1145. a_17_1·a_23_3
  1146. a_19_0·a_21_3
  1147. a_19_0·a_21_4
  1148. a_19_1·a_21_3
  1149. a_19_1·a_21_4
  1150. a_19_2·a_21_3
  1151. a_19_2·a_21_4
  1152. a_19_3·a_21_3
  1153. a_19_3·a_21_4
  1154. c_24_5·a_17_0 + c_24_4·a_17_1 + c_24_4·a_17_0 + c_16_0·a_25_1 + c_16_02·a_9_2
  1155. c_24_5·a_17_1 + c_24_4·a_17_0 + c_16_0·a_25_1 + c_16_0·a_25_0 + c_16_02·a_9_2
       + c_16_02·a_9_0
  1156. a_18_0·a_23_2
  1157. a_18_0·a_23_3
  1158. a_18_1·a_23_2
  1159. a_18_1·a_23_3
  1160. a_18_2·a_23_2
  1161. a_18_2·a_23_3
  1162. a_18_3·a_23_2
  1163. a_18_3·a_23_3
  1164. a_20_0·a_21_3
  1165. a_20_0·a_21_4
  1166. a_20_1·a_21_3
  1167. a_20_1·a_21_4
  1168. a_20_2·a_21_3
  1169. a_20_2·a_21_4
  1170. a_20_3·a_21_3
  1171. a_20_3·a_21_4
  1172. a_26_0·a_15_0
  1173. a_26_0·a_15_1
  1174. a_26_1·a_15_0
  1175. a_26_1·a_15_1
  1176. a_26_2·a_15_0
  1177. a_26_2·a_15_1
  1178. a_26_3·a_15_0
  1179. a_26_3·a_15_1
  1180. a_18_1·c_24_4 + a_18_0·c_24_5 + c_16_0·a_26_1 + c_16_0·a_26_0
  1181. a_18_1·c_24_5 + a_18_0·c_24_5 + a_18_0·c_24_4 + c_16_0·a_26_1
  1182. a_18_3·c_24_4 + a_18_2·c_24_5 + c_16_0·a_26_3 + c_16_0·a_26_2
  1183. a_18_3·c_24_5 + a_18_2·c_24_5 + a_18_2·c_24_4 + c_16_0·a_26_3
  1184. a_15_0·a_27_0
  1185. a_15_0·a_27_1
  1186. a_15_1·a_27_0
  1187. a_15_1·a_27_1
  1188. a_17_0·a_25_0
  1189. a_17_0·a_25_1
  1190. a_17_1·a_25_0
  1191. a_17_1·a_25_1
  1192. a_19_0·a_23_2
  1193. a_19_0·a_23_3
  1194. a_19_1·a_23_2
  1195. a_19_1·a_23_3
  1196. a_19_2·a_23_2
  1197. a_19_2·a_23_3
  1198. a_19_3·a_23_2
  1199. a_19_3·a_23_3
  1200. a_21_32
  1201. a_21_3·a_21_4
  1202. a_21_42
  1203. c_24_5·a_19_0 + c_24_4·a_19_3 + c_24_4·a_19_1 + c_24_4·a_19_0 + c_16_0·a_27_1
       + c_16_02·a_11_1
  1204. c_24_5·a_19_1 + c_24_4·a_19_2 + c_24_4·a_19_0 + c_16_0·a_27_1 + c_16_0·a_27_0
       + c_16_02·a_11_0
  1205. c_24_5·a_19_2 + c_24_4·a_19_3 + c_24_4·a_19_2 + c_16_02·a_11_1
  1206. c_24_5·a_19_3 + c_24_4·a_19_2 + c_16_02·a_11_1 + c_16_02·a_11_0
  1207. a_18_0·a_25_0
  1208. a_18_0·a_25_1
  1209. a_18_1·a_25_0
  1210. a_18_1·a_25_1
  1211. a_18_2·a_25_0
  1212. a_18_2·a_25_1
  1213. a_18_3·a_25_0
  1214. a_18_3·a_25_1
  1215. a_20_0·a_23_2
  1216. a_20_0·a_23_3
  1217. a_20_1·a_23_2
  1218. a_20_1·a_23_3
  1219. a_20_2·a_23_2
  1220. a_20_2·a_23_3
  1221. a_20_3·a_23_2
  1222. a_20_3·a_23_3
  1223. a_26_0·a_17_0
  1224. a_26_0·a_17_1
  1225. a_26_1·a_17_0
  1226. a_26_1·a_17_1
  1227. a_26_2·a_17_0
  1228. a_26_2·a_17_1
  1229. a_26_3·a_17_0
  1230. a_26_3·a_17_1
  1231. a_20_1·c_24_4 + a_20_0·c_24_5 + a_20_0·c_24_4 + a_12_1·c_16_02
  1232. a_20_1·c_24_5 + a_20_0·c_24_4 + a_12_1·c_16_02 + a_12_0·c_16_02
  1233. a_20_3·c_24_4 + a_20_2·c_24_5 + a_20_2·c_24_4 + a_12_3·c_16_02
  1234. a_20_3·c_24_5 + a_20_2·c_24_4 + a_12_3·c_16_02 + a_12_2·c_16_02
  1235. a_18_0·a_26_0
  1236. a_18_0·a_26_1
  1237. a_18_0·a_26_2
  1238. a_18_0·a_26_3
  1239. a_18_1·a_26_0
  1240. a_18_1·a_26_1
  1241. a_18_1·a_26_2
  1242. a_18_1·a_26_3
  1243. a_18_2·a_26_0
  1244. a_18_2·a_26_1
  1245. a_18_2·a_26_2
  1246. a_18_2·a_26_3
  1247. a_18_3·a_26_0
  1248. a_18_3·a_26_1
  1249. a_18_3·a_26_2
  1250. a_18_3·a_26_3
  1251. a_17_0·a_27_0
  1252. a_17_0·a_27_1
  1253. a_17_1·a_27_0
  1254. a_17_1·a_27_1
  1255. a_19_0·a_25_0
  1256. a_19_0·a_25_1
  1257. a_19_1·a_25_0
  1258. a_19_1·a_25_1
  1259. a_19_2·a_25_0
  1260. a_19_2·a_25_1
  1261. a_19_3·a_25_0
  1262. a_19_3·a_25_1
  1263. a_21_3·a_23_2
  1264. a_21_3·a_23_3
  1265. a_21_4·a_23_2
  1266. a_21_4·a_23_3
  1267. c_24_5·a_21_3 + c_24_4·a_21_4 + c_16_02·a_13_1 + c_16_02·a_13_0
  1268. c_24_5·a_21_4 + c_24_4·a_21_4 + c_24_4·a_21_3 + c_16_02·a_13_0
  1269. a_18_0·a_27_0
  1270. a_18_0·a_27_1
  1271. a_18_1·a_27_0
  1272. a_18_1·a_27_1
  1273. a_18_2·a_27_0
  1274. a_18_2·a_27_1
  1275. a_18_3·a_27_0
  1276. a_18_3·a_27_1
  1277. a_20_0·a_25_0
  1278. a_20_0·a_25_1
  1279. a_20_1·a_25_0
  1280. a_20_1·a_25_1
  1281. a_20_2·a_25_0
  1282. a_20_2·a_25_1
  1283. a_20_3·a_25_0
  1284. a_20_3·a_25_1
  1285. a_26_0·a_19_0
  1286. a_26_0·a_19_1
  1287. a_26_0·a_19_2
  1288. a_26_0·a_19_3
  1289. a_26_1·a_19_0
  1290. a_26_1·a_19_1
  1291. a_26_1·a_19_2
  1292. a_26_1·a_19_3
  1293. a_26_2·a_19_0
  1294. a_26_2·a_19_1
  1295. a_26_2·a_19_2
  1296. a_26_2·a_19_3
  1297. a_26_3·a_19_0
  1298. a_26_3·a_19_1
  1299. a_26_3·a_19_2
  1300. a_26_3·a_19_3
  1301. a_20_0·a_26_0
  1302. a_20_0·a_26_1
  1303. a_20_0·a_26_2
  1304. a_20_0·a_26_3 + a_6_0·a_8_0·c_16_02
  1305. a_20_1·a_26_0
  1306. a_20_1·a_26_1
  1307. a_20_1·a_26_2 + a_6_0·a_8_0·c_16_02
  1308. a_20_1·a_26_3
  1309. a_20_2·a_26_0
  1310. a_20_2·a_26_1 + a_6_0·a_8_0·c_16_02
  1311. a_20_2·a_26_2
  1312. a_20_2·a_26_3
  1313. a_20_3·a_26_0 + a_6_0·a_8_0·c_16_02
  1314. a_20_3·a_26_1
  1315. a_20_3·a_26_2
  1316. a_20_3·a_26_3
  1317. a_19_0·a_27_0
  1318. a_19_0·a_27_1 + a_6_0·a_8_0·c_16_02
  1319. a_19_1·a_27_0 + a_6_0·a_8_0·c_16_02
  1320. a_19_1·a_27_1
  1321. a_19_2·a_27_0 + a_6_0·a_8_0·c_16_02
  1322. a_19_2·a_27_1 + a_6_0·a_8_0·c_16_02
  1323. a_19_3·a_27_0 + a_6_0·a_8_0·c_16_02
  1324. a_19_3·a_27_1
  1325. a_21_3·a_25_0
  1326. a_21_3·a_25_1 + a_6_0·a_8_0·c_16_02
  1327. a_21_4·a_25_0 + a_6_0·a_8_0·c_16_02
  1328. a_21_4·a_25_1
  1329. a_23_22
  1330. a_23_2·a_23_3
  1331. a_23_32
  1332. c_24_5·a_23_2 + c_24_4·a_23_3 + c_16_0·c_24_5·a_7_0 + c_16_0·c_24_4·a_7_1
       + c_16_02·a_15_1 + c_16_02·a_15_0
  1333. c_24_5·a_23_3 + c_24_4·a_23_3 + c_24_4·a_23_2 + c_16_0·c_24_5·a_7_1
       + c_16_0·c_24_4·a_7_1 + c_16_0·c_24_4·a_7_0 + c_16_02·a_15_0
  1334. a_20_0·a_27_0
  1335. a_20_0·a_27_1
  1336. a_20_1·a_27_0
  1337. a_20_1·a_27_1
  1338. a_20_2·a_27_0
  1339. a_20_2·a_27_1
  1340. a_20_3·a_27_0
  1341. a_20_3·a_27_1
  1342. a_26_0·a_21_3
  1343. a_26_0·a_21_4
  1344. a_26_1·a_21_3
  1345. a_26_1·a_21_4
  1346. a_26_2·a_21_3
  1347. a_26_2·a_21_4
  1348. a_26_3·a_21_3
  1349. a_26_3·a_21_4
  1350. c_24_52 + c_24_4·c_24_5 + c_24_42 + a_8_3·c_16_0·c_24_5 + a_8_1·c_16_0·c_24_4
       + c_16_03
  1351. a_21_3·a_27_0
  1352. a_21_3·a_27_1
  1353. a_21_4·a_27_0
  1354. a_21_4·a_27_1
  1355. a_23_2·a_25_0
  1356. a_23_2·a_25_1
  1357. a_23_3·a_25_0
  1358. a_23_3·a_25_1
  1359. c_24_5·a_25_0 + c_24_4·a_25_1 + c_16_0·c_24_5·a_9_0 + c_16_0·c_24_4·a_9_2
       + c_16_02·a_17_1 + c_16_02·a_17_0
  1360. c_24_5·a_25_1 + c_24_4·a_25_1 + c_24_4·a_25_0 + c_16_0·c_24_5·a_9_2
       + c_16_0·c_24_4·a_9_2 + c_16_0·c_24_4·a_9_0 + c_16_02·a_17_0
  1361. a_26_0·a_23_2
  1362. a_26_0·a_23_3
  1363. a_26_1·a_23_2
  1364. a_26_1·a_23_3
  1365. a_26_2·a_23_2
  1366. a_26_2·a_23_3
  1367. a_26_3·a_23_2
  1368. a_26_3·a_23_3
  1369. c_24_5·a_26_0 + c_24_4·a_26_1 + c_24_4·a_26_0 + c_16_02·a_18_1
  1370. c_24_5·a_26_1 + c_24_4·a_26_0 + c_16_02·a_18_1 + c_16_02·a_18_0
  1371. c_24_5·a_26_2 + c_24_4·a_26_3 + c_24_4·a_26_2 + c_16_02·a_18_3
  1372. c_24_5·a_26_3 + c_24_4·a_26_2 + c_16_02·a_18_3 + c_16_02·a_18_2
  1373. a_23_2·a_27_0
  1374. a_23_2·a_27_1
  1375. a_23_3·a_27_0
  1376. a_23_3·a_27_1
  1377. a_25_02
  1378. a_25_0·a_25_1
  1379. a_25_12
  1380. c_24_5·a_27_0 + c_24_4·a_27_1 + c_16_0·c_24_4·a_11_1 + c_16_02·a_19_3 + c_16_02·a_19_1
       + c_16_02·a_19_0
  1381. c_24_5·a_27_1 + c_24_4·a_27_1 + c_24_4·a_27_0 + c_16_0·c_24_4·a_11_0 + c_16_02·a_19_2
       + c_16_02·a_19_0
  1382. a_26_0·a_25_0
  1383. a_26_0·a_25_1
  1384. a_26_1·a_25_0
  1385. a_26_1·a_25_1
  1386. a_26_2·a_25_0
  1387. a_26_2·a_25_1
  1388. a_26_3·a_25_0
  1389. a_26_3·a_25_1
  1390. a_26_02
  1391. a_26_0·a_26_1
  1392. a_26_0·a_26_2
  1393. a_26_0·a_26_3
  1394. a_26_12
  1395. a_26_1·a_26_2
  1396. a_26_1·a_26_3
  1397. a_26_22
  1398. a_26_2·a_26_3
  1399. a_26_32
  1400. a_25_0·a_27_0
  1401. a_25_0·a_27_1
  1402. a_25_1·a_27_0
  1403. a_25_1·a_27_1
  1404. a_26_0·a_27_0
  1405. a_26_0·a_27_1
  1406. a_26_1·a_27_0
  1407. a_26_1·a_27_1
  1408. a_26_2·a_27_0
  1409. a_26_2·a_27_1
  1410. a_26_3·a_27_0
  1411. a_26_3·a_27_1
  1412. a_27_02
  1413. a_27_0·a_27_1 + a_6_0·a_8_0·c_16_0·c_24_5
  1414. a_27_12

About the group Ring generators Ring relations Completion information Restriction maps

Data used for the Hilbert-Poincaré test

  • We proved completion in degree 54 using the Hilbert-Poincaré criterion.
  • The completion test was perfect: It applied in the last degree in which a generator or relation was found.
  • The following is a filter regular homogeneous system of parameters:
    1. c_16_0, an element of degree 16
    2. c_24_5, an element of degree 24
  • The above filter regular HSOP forms a Duflot regular sequence.
  • The Raw Filter Degree Type of the filter regular HSOP is [-1, -1, 38].

About the group Ring generators Ring relations Completion information Restriction maps

Restriction maps

Expressing the generators as elements of H*(SmallGroup(960,5748); GF(2))

  1. a_5_0 → a_5_0
  2. a_5_1 → a_5_1
  3. a_5_2 → a_5_2
  4. a_6_0 → a_6_0
  5. a_6_1 → a_6_1
  6. a_6_2 → a_6_2
  7. a_6_3 → a_6_3
  8. a_7_0 → a_7_0
  9. a_7_1 → a_7_1
  10. a_8_0 → a_8_0
  11. a_8_1 → a_8_1
  12. a_8_2 → a_8_2
  13. a_8_3 → a_8_3
  14. a_9_0 → a_9_0
  15. a_9_1 → a_9_1
  16. a_9_2 → a_9_2
  17. a_11_0 → a_11_0
  18. a_11_1 → a_11_1
  19. a_12_0 → a_12_0
  20. a_12_1 → a_12_1
  21. a_12_2 → a_12_2
  22. a_12_3 → a_12_3
  23. a_13_0 → a_13_0
  24. a_13_1 → a_13_1
  25. a_15_0 → a_15_0
  26. a_15_1 → a_15_1
  27. c_16_0 → c_16_0
  28. a_17_0 → a_17_0
  29. a_17_1 → a_17_1
  30. a_18_0 → a_18_0
  31. a_18_1 → a_18_1
  32. a_18_2 → a_18_2
  33. a_18_3 → a_18_3
  34. a_19_0 → a_19_0
  35. a_19_1 → a_19_1
  36. a_19_2 → a_19_2
  37. a_19_3 → a_19_3
  38. a_20_0 → a_20_0
  39. a_20_1 → a_20_1
  40. a_20_2 → a_20_2
  41. a_20_3 → a_20_3
  42. a_21_3 → a_21_3
  43. a_21_4 → a_21_4
  44. a_23_2 → a_23_2
  45. a_23_3 → a_23_3
  46. c_24_4 → c_24_4
  47. c_24_5 → c_24_5
  48. a_25_0 → a_25_0
  49. a_25_1 → a_25_1
  50. a_26_0 → a_26_0
  51. a_26_1 → a_26_1
  52. a_26_2 → a_26_2
  53. a_26_3 → a_26_3
  54. a_27_0 → a_27_0
  55. a_27_1 → a_27_1

Restriction map to the greatest el. ab. subgp. in the centre of a Sylow subgroup, which is of rank 2

  1. a_5_0 → 0, an element of degree 5
  2. a_5_1 → 0, an element of degree 5
  3. a_5_2 → 0, an element of degree 5
  4. a_6_0 → 0, an element of degree 6
  5. a_6_1 → 0, an element of degree 6
  6. a_6_2 → 0, an element of degree 6
  7. a_6_3 → 0, an element of degree 6
  8. a_7_0 → 0, an element of degree 7
  9. a_7_1 → 0, an element of degree 7
  10. a_8_0 → 0, an element of degree 8
  11. a_8_1 → 0, an element of degree 8
  12. a_8_2 → 0, an element of degree 8
  13. a_8_3 → 0, an element of degree 8
  14. a_9_0 → 0, an element of degree 9
  15. a_9_1 → 0, an element of degree 9
  16. a_9_2 → 0, an element of degree 9
  17. a_11_0 → 0, an element of degree 11
  18. a_11_1 → 0, an element of degree 11
  19. a_12_0 → 0, an element of degree 12
  20. a_12_1 → 0, an element of degree 12
  21. a_12_2 → 0, an element of degree 12
  22. a_12_3 → 0, an element of degree 12
  23. a_13_0 → 0, an element of degree 13
  24. a_13_1 → 0, an element of degree 13
  25. a_15_0 → 0, an element of degree 15
  26. a_15_1 → 0, an element of degree 15
  27. c_16_0 → c_1_116 + c_1_08·c_1_18 + c_1_016, an element of degree 16
  28. a_17_0 → 0, an element of degree 17
  29. a_17_1 → 0, an element of degree 17
  30. a_18_0 → 0, an element of degree 18
  31. a_18_1 → 0, an element of degree 18
  32. a_18_2 → 0, an element of degree 18
  33. a_18_3 → 0, an element of degree 18
  34. a_19_0 → 0, an element of degree 19
  35. a_19_1 → 0, an element of degree 19
  36. a_19_2 → 0, an element of degree 19
  37. a_19_3 → 0, an element of degree 19
  38. a_20_0 → 0, an element of degree 20
  39. a_20_1 → 0, an element of degree 20
  40. a_20_2 → 0, an element of degree 20
  41. a_20_3 → 0, an element of degree 20
  42. a_21_3 → 0, an element of degree 21
  43. a_21_4 → 0, an element of degree 21
  44. a_23_2 → 0, an element of degree 23
  45. a_23_3 → 0, an element of degree 23
  46. c_24_4 → c_1_124 + c_1_016·c_1_18 + c_1_024, an element of degree 24
  47. c_24_5 → c_1_124 + c_1_08·c_1_116 + c_1_024, an element of degree 24
  48. a_25_0 → 0, an element of degree 25
  49. a_25_1 → 0, an element of degree 25
  50. a_26_0 → 0, an element of degree 26
  51. a_26_1 → 0, an element of degree 26
  52. a_26_2 → 0, an element of degree 26
  53. a_26_3 → 0, an element of degree 26
  54. a_27_0 → 0, an element of degree 27
  55. a_27_1 → 0, an element of degree 27

About the group Ring generators Ring relations Completion information Restriction maps


Simon King
Department of Mathematics and Computer Science
Friedrich-Schiller-Universität Jena
07737 Jena
GERMANY
E-mail: simon dot king at uni hyphen jena dot de
Tel: +49 (0)3641 9-46161
Fax: +49 (0)3641 9-46162
Office: Zi. 3529, Ernst-Abbe-Platz 2

Last change: 14.12.2010