/* Group 10871635968.b downloaded from the LMFDB on 23 July 2026. */ /* Various presentations of this group are stored in this file: GPC is polycyclic presentation GPerm is permutation group GLZ, GLFp, GLZA, GLZq, GLFq if they exist are matrix groups Many characteristics of the group are stored as booleans in a record: Agroup, Zgroup, abelian, almost_simple,cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable */ /* Constructions */ GPC := PCGroup([31, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 308120618552, 316874064621, 88377399072, 442914669878, 128330943135, 250, 215511005027, 613557444626, 126804844384, 920166529684, 255863022315, 256874070606, 205153537027, 438, 1423697216837, 968144109252, 438067475347, 206833893578, 51663464320, 114515406662, 1175638233541, 538899025684, 218006867947, 2815320806, 55085349907, 16212599672, 1786005474055, 19915026982, 493544421125, 150062994660, 6083, 50242384642, 3559215345, 25927136, 1362986691848, 19869621159, 103736485510, 17680966661, 113045358516, 53039554075, 18808636766, 87023115, 814, 2902115363849, 473583736360, 407987260231, 34867470822, 17081773893, 15021186564, 51427955, 922357489162, 1394784672553, 580166029768, 20180172775, 132556422726, 86532760325, 25258088436, 19800858139, 1993984118, 2724588243, 1002, 1911758782475, 1011144425514, 568729313353, 1419909224, 202937249415, 487445158, 135789125, 38902500, 12673933123, 17841410, 3688777617420, 1433633670187, 949574366282, 2045615209, 156154414344, 23490554215, 230709638, 56439573, 13742638780, 18391599, 1371574552, 1719399047, 1190, 921765003277, 1179604500524, 27758223435, 762173546, 237081437065, 316674344, 194432199, 4923526, 14764697621, 17457508, 10129883, 2393430, 451109222414, 909797007405, 818513326156, 351740344427, 179455478538, 54761227369, 54243090920, 13704234711, 6231867022, 636555533, 3082244454, 567247810, 794081816, 805332, 1378, 4951048207, 2163517653038, 3704143949, 250196557932, 89548554379, 55952990378, 78990373065, 16620936424, 15552147719, 3949604646, 71749, 281131203, 2584923633680, 180299634735, 862971353678, 354825575533, 152820826124, 3145405995, 56168351626, 42328960649, 3112243032, 2110217911, 1935470, 911013, 338100400, 1518179, 19430940, 53427214, 1566, 19255910417, 2431543799856, 1220014485583, 340682195054, 263629126797, 8901716140, 77022213323, 1300417002, 15737260873, 11108825000, 482439, 262309493, 92572651, 10288886, 4477372858386, 1025543503921, 1119343214672, 643506455919, 321777655054, 563856941, 37658508, 18829387, 9414842, 32060745, 2290360, 1336211, 890958, 382093, 4976321495059, 1053189734450, 1171673579601, 2725539952, 337894802063, 168713844654, 84537982285, 42326309036, 21134495787, 28927018, 402089, 1004760, 2410951, 1071782, 4616920498196, 2308460249139, 186612056146, 708715139441, 863944848, 704205103, 352102670, 95056653, 88025884, 18983490, 6117157, 2672096, 1617507, 4054780477461, 2548719157300, 347552612435, 2715254898, 1022934673, 791949488, 395974863, 98993933, 14584219, 10827794, 2431041, 1804996, 817538531350, 1937869111349, 1264156803156, 1005364339, 1542544274, 416437809, 208219024, 192818255, 52054974, 24025580, 4620603, 308410, 1386497, 6501896994839, 1028505654, 1619406065749, 469985919092, 43444076691, 25671499954, 83432374481, 2962096368, 20240990479, 10429047086, 1326772557, 73710025, 76709864, 24141831, 8928550, 6759867340824, 3386361830455, 1799884886, 106964582517, 246841344148, 169703424179, 11827814610, 1285632241, 15556147472, 1478477103, 578534734, 106243658, 52229289, 2678920, 6101351, 89137177, 3521058637880, 1760239623255, 517708578934, 38507249813, 8557166772, 117661040851, 3743760626, 2005586193, 14707630384, 3075232079, 63139275, 76138474, 1857545, 619560, 7316207732762, 3655882294329, 300837976, 97749172343, 11107860630, 4443144373, 66647163092, 4165447923, 1943875858, 8330895665, 833089872, 23141836, 57853931, 643338, 964777, 7568843563035, 8975425594, 1151926361, 124408037496, 258031485079, 184308203702, 55292461269, 32829898996, 16558940435, 6911557938, 95994317, 55996908, 10666507, 6666794, 29230129180, 17597730875, 8351465562, 668117237881, 458137534616, 171801575607, 85900787926, 19685597429, 22519130388, 10737598771, 149133774, 91137517, 30379532, 12428331, 8116777635869, 4049132267580, 4628275291, 207346729082, 39494615193, 138231152824, 78989230295, 11416412406, 13730550037, 9873654068, 3085517139, 239985103, 85709294, 14285325, 1429036, 8369588312094, 12487772221, 1753602140, 1300853883003, 40811102424, 73013612791, 7811500310, 5101388085, 6376735060, 230271440, 44283375, 17713678, 20665901]); a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x := Explode([GPC.1, GPC.2, GPC.3, GPC.5, GPC.7, GPC.8, GPC.9, GPC.11, GPC.13, GPC.15, GPC.17, GPC.19, GPC.20, GPC.21, GPC.22, GPC.23, GPC.24, GPC.25, GPC.26, GPC.27, GPC.28, GPC.29, GPC.30, GPC.31]); AssignNames(~GPC, ["a", "b", "c", "c2", "d", "d2", "e", "f", "g", "g2", "h", "h2", "i", "i2", "j", "j2", "k", "k2", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x"]); GPerm := PermutationGroup< 36 | (1,25,7,30,17,28,11,36)(2,26,8,29,18,27,12,35)(3,24,4,23)(5,31,9,34,14,21,15,20)(6,32,10,33,13,22,16,19), (1,14,12,8,15,4,17,9,2,13,11,7,16,3,18,10)(19,23,25,22,20,24,26,21)(27,29,35,34,28,30,36,33)(31,32), (1,22,7,20,4,27,15,24)(2,21,8,19,3,28,16,23)(5,31,13,35,11,30,9,26)(6,32,14,36,12,29,10,25)(17,34)(18,33), (1,36,6,31,10,34,15,27,8,29,4,21,18,19,11,25,2,35,5,32,9,33,16,28,7,30,3,22,17,20,12,26)(13,24,14,23) >; /* Booleans */ RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable : BoolElt >; booleans_10871635968_b := rec< RF | Agroup := false, Zgroup := false, abelian := false, almost_simple := false, cyclic := false, metabelian := false, metacyclic := false, nilpotent := false, perfect := false, quasisimple := false, rational := false, solvable := true, supersolvable := false>;