/* Group 104485552128.hw downloaded from the LMFDB on 08 November 2025. */ /* 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([29, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2034683458356, 4365430078373, 146, 4941847708142, 741299332668, 3965140501203, 3215479958456, 2998426785613, 322, 10244997062044, 2815318032093, 1520368642742, 373812134520, 9805893870605, 8436429700918, 4523078358081, 721981742036, 713954083285, 498, 1854720145326, 3487756176359, 4839545022250, 104532438453, 452326172966, 217929484148, 16603847053255, 668127430020, 1447167934769, 1531324489438, 886815291451, 339544050232, 246756315173, 674, 3928465294856, 13175325418213, 5982287273922, 897167304959, 480769754956, 187835847489, 234971678090, 44228550768, 22889800759929, 5953060621958, 4100938223587, 1896018385376, 837874078525, 532662520634, 204962091463, 107882342252, 61962572421, 850, 12607539314314, 16072690360359, 2008198964708, 2521523362785, 922189188926, 5196331515, 271470740648, 168549144669, 54057123934, 938, 22528212811787, 9493441781800, 220986703941, 1001945029730, 56343616639, 30192324252, 140642401750, 5811, 31042833289740, 5538913042613, 668988827668, 140194827235, 1612819318784, 680918230461, 307734966426, 69357981063, 89183068972, 42055126893, 16923200804, 951778678, 1114, 25860502413325, 2572035594282, 5329584164423, 2813143105124, 1224432910977, 76106304670, 166692712891, 148945699384, 72435532085, 45259564834, 22920231735, 6113577139214, 6907597650223, 4193808606882, 2418054336101, 145482151810, 780972760959, 18879445628, 148311600697, 451070886, 37023779435, 56454604, 1098212643, 4225958372, 1290, 15831610392591, 23989421359148, 1631499546697, 3310417428582, 82210406531, 571365531808, 18935654589, 220182239450, 9583151863, 54901237524, 1284537905, 3179918571, 13630748914576, 662048278233, 12704300049002, 2220395202535, 146236704900, 410616544961, 437222690110, 114742098075, 84410482136, 57607310581, 138541194, 1242129611, 4646905960, 1731504147, 730599800, 297529402, 1466, 21224075673617, 24081490076590, 5835885366603, 640533187688, 1782114214021, 855234243234, 44426092223, 71593010140, 661177977, 58391705366, 296087059, 660388800, 499003133, 120438322, 39394719, 20073440, 1554, 42487637999634, 24644058513455, 3613028696140, 1522431513705, 1450070632070, 409156272931, 27154690752, 62524341725, 6788672890, 45314707527, 2931602420, 488600718, 40339887390739, 25337083441968, 677546979917, 2088219472106, 194065735815, 1103458523844, 209387980993, 53603804382, 1761938171, 13256628760, 10122123189, 2571497618, 2160078127, 440610156, 43806665, 22321174, 954003, 7868792, 3572761, 1730, 4771650207764, 1440223690801, 12438295511118, 49704689829, 101025986, 12325146847, 25256700, 12628505, 256774256, 42796074, 7133092, 15129, 20317665029397, 15663391045682, 9672125956495, 4586286601004, 2461969686665, 256486131606, 510449651907, 24077813984, 114025646845, 80475462426, 20608359863, 2832781588, 5412547377, 1370087534, 946741387, 339972792, 127212581, 4663018, 3939555, 708752, 1906, 5300448067606, 32089498490931, 13949986931792, 5753659501, 59306950823, 27661824196, 14494796001, 165971198, 3457728283, 10373554, 1729292, 320646, 96563, 664905, 2831955001367, 6237507723316, 382435541073, 457675702382, 117998125224, 1154580677, 230916322, 519561471, 144322844, 3608435, 601773, 8352487, 301188, 727198, 45790661836824, 14911406899253, 15404990054482, 2414036467311, 1064379436969, 65005286598, 115848921827, 1623629056, 413424285, 957488, 4698517, 1566575, 261633, 70358762852377, 13925859317814, 6889426891859, 1252394916976, 1180001072810, 74422333639, 284493441252, 18855742721, 64744303390, 3728934459, 132897397, 22149935, 25986345, 1629158, 353448, 91114, 3329348272154, 6677400748087, 18124373459028, 506052624497, 129370742955, 31628289224, 15814144741, 15781672194, 3953536415, 9152194, 9133431, 23935868780571, 22655640010808, 5983967195221, 6017554321522, 853465890959, 1505958481836, 167433412809, 227981537510, 62433939715, 103972377888, 11895787325, 55112555, 23678440, 6811634, 921444, 52005571230748, 37386932355129, 20121518086742, 7045535334003, 2496145268880, 1363030741101, 346547331274, 173273665767, 113632367876, 102645813025, 56580757950, 261948444, 10960491, 2452993]); a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q := Explode([GPC.1, GPC.2, GPC.4, GPC.6, GPC.8, GPC.10, GPC.13, GPC.15, GPC.17, GPC.20, GPC.22, GPC.24, GPC.25, GPC.26, GPC.27, GPC.28, GPC.29]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "d", "d2", "e", "e2", "f", "f2", "f4", "g", "g2", "h", "h2", "i", "i2", "i4", "j", "j2", "k", "k2", "l", "m", "n", "o", "p", "q"]); GPerm := PermutationGroup< 36 | (2,3)(4,33)(5,32,6,31)(7,34,8,36)(9,35)(10,12,11)(13,22,14,24)(15,23)(16,26,18,25,17,27)(19,20)(29,30), (1,29,3,30)(2,28)(4,35,14,8)(5,36,13,7,6,34,15,9)(10,19,12,20,11,21)(16,31,26,22)(17,32,27,23,18,33,25,24), (1,33,20,13,3,32,19,15)(2,31,21,14)(4,29,23,10,5,30,24,11,6,28,22,12)(7,18,8,16,9,17)(25,34,26,35,27,36) >; /* Booleans */ RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable : BoolElt >; booleans_104485552128_hw := 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>;