/* Group 1358954496.by 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([28, 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, 2, 56, 35071498365, 7942137842, 43106805366, 24584636218, 3582163203, 43980497375, 37485300443, 311, 73052125444, 73821960832, 7624844140, 114660676037, 55183954593, 26897841661, 4749489785, 6995675013, 481, 234798143558, 75696699042, 32537659006, 29648623738, 5944994502, 566, 217894699015, 92321417251, 50933270591, 19661738075, 1181057143, 6284811464, 143858873124, 47873347264, 21060559388, 16874385816, 1535584324, 2417916488, 2406997608, 736, 259859496969, 12500508197, 75325241665, 31086025693, 4376359801, 8302701269, 1512336177, 776655805, 189846981, 166028380682, 8177799206, 66248050242, 13070534494, 16579221242, 10984571286, 1708694242, 2661275438, 552319386, 276158914, 906, 86027, 162622881831, 791949379, 22640615519, 5538710167, 48563, 2403307, 412741991, 160380752908, 165772938280, 56999045444, 48751597536, 17899382716, 3129104312, 712294308, 3476812456, 650607284, 206591376, 147645244, 41659028, 1076, 238038707213, 8206184489, 52332263493, 2709601, 504024345, 5724335413, 989279661, 56713, 89856101, 45259857, 327131965454, 236557117482, 99057530950, 12382191514, 3435203702, 572443438, 15901550, 7952238, 390595903503, 35022274603, 106009731143, 1321850979, 30962857087, 12219476123, 7740956343, 3060384979, 1305118319, 150333387, 181795111, 109533635, 30302175, 15709051, 379040643088, 20689869356, 16182415944, 25233925348, 18076286720, 16023873756, 6210600664, 505700708, 943285632, 360139012, 193260104, 116328060, 32210320, 19388336, 440615282705, 283847639085, 4567062601, 130636957, 8938823225, 1489695217, 212847561, 106487461, 41407985, 20692101, 252313657362, 165342740014, 119201435210, 27711718374, 20147750914, 17848361822, 1947413850, 569331718, 685622690, 401359158, 224978842, 108687926, 76962, 21816106, 467784253459, 315200471087, 156915118155, 66044160103, 16511040159, 9807195067, 759508083, 229320299, 114327687, 21097795, 10547423, 763194120212, 303553184304, 96828867148, 30805536488, 22512422148, 17023390432, 7552276892, 598779432, 1920932740, 440559272, 288075612, 120350992, 1693796, 23899056, 321633607701, 298194462769, 156474920525, 28098233961, 15829539425, 3891954717, 1162809865, 360582005, 1080880689, 305851693, 4080713, 49545237, 24667489, 709417046038, 11818275890, 158472841038, 28921390954, 16744365954, 13410808174, 1162248914, 2269482006, 1121108962, 309483518, 75893154, 25556854, 11897642, 614910320663, 75513876531, 143491461199, 105931349099, 56788688007, 25895697571, 6452151743, 3924329691, 2104631671, 418116659, 169029807, 82664395, 27700199, 13963203, 252249984024, 270403660852, 90365587280, 58184784108, 19608220936, 14878231364, 5647849392, 2405932420, 56473448, 1165380576, 260643904, 135399932, 53210160, 2167588, 156941051929, 426381097013, 69282210897, 84291847021, 43527190025, 4118325285, 2906414977, 7256602301, 541811337, 1209394645, 54722609, 32131341, 68757049, 4490693, 22014913562, 7809467958, 129104430418, 57419445998, 29604911754, 26955760774, 8069027090, 90180438, 339002746, 263362706, 62896482, 209155294, 10483058, 34859550, 1037490757659, 112075923511, 73214862419, 53713884783, 22962199847, 8378040579, 5918869375, 1466011259, 408768499, 49533455, 14992011, 20359303]); a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u := Explode([GPC.1, GPC.3, GPC.4, GPC.6, GPC.9, GPC.11, GPC.13, GPC.15, GPC.16, GPC.17, GPC.18, GPC.19, GPC.20, GPC.21, GPC.22, GPC.23, GPC.24, GPC.25, GPC.26, GPC.27, GPC.28]); AssignNames(~GPC, ["a", "a2", "b", "c", "c2", "d", "d2", "d4", "e", "e2", "f", "f2", "g", "g2", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u"]); GPerm := PermutationGroup< 36 | (1,23,10,36,18,33,4,20,15,21,8,28,11,29,13,25)(2,24,9,35,17,34,3,19,16,22,7,27,12,30,14,26)(5,31)(6,32), (1,17,2,18)(3,4)(7,10,8,9)(11,15,12,16)(13,14)(19,35,33,32,23,27)(20,36,34,31,24,28)(21,25,30,22,26,29), (1,9,17,4,16,8,11,14)(2,10,18,3,15,7,12,13)(5,6)(19,21,28,29,26,23,35,34,20,22,27,30,25,24,36,33) >; /* Booleans */ RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable : BoolElt >; booleans_1358954496_by := 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>;