/* Group 5435817984.t 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([30, 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, 120388780320, 288135854761, 151, 419673699722, 94502308382, 526335226563, 188630883393, 162257163663, 333, 750385701604, 337933225234, 4749965464, 10894824124, 141450157445, 357498044675, 38570277665, 106813157135, 669882725, 30137650715, 144364214406, 406360893156, 245932434786, 124615349136, 25973204166, 25721379336, 606, 879585884167, 553722854437, 245072186947, 100855453537, 67944347647, 30389945437, 8361394777, 34758218888, 293806491878, 86031262148, 65005675298, 21835288928, 43252123118, 3585177908, 1187300918, 788, 842375155209, 722183673639, 294520972869, 69081580899, 76452643329, 3743515359, 6930736989, 12113207019, 879, 258425671690, 152735109160, 13610403910, 27744330340, 10675125250, 4040826400, 2841638110, 1882540, 77181419531, 114557091881, 233663201351, 20802908261, 17621176451, 8776373921, 4372047551, 6956453021, 449072891, 2479583081, 24071, 1061, 153093857292, 77515975722, 293031198792, 91952742, 7850119812, 3908885922, 5649508992, 15954756702, 1416598812, 1550952282, 1928667955213, 644095979563, 279301585993, 13333931623, 26175018373, 10562482723, 8390860993, 7615369663, 1006120333, 2906187763, 163035493, 1243, 1384676352014, 370245657644, 323968089674, 12909081704, 17541619334, 5346417764, 4993135394, 17349293024, 1450883054, 1443166484, 229943114, 221088153615, 124229222445, 333224017995, 558121065, 23423754375, 4789186725, 19642014915, 6438113505, 1746409215, 3309984285, 484185, 216375, 81045, 36435, 1425, 14254018576, 133439370286, 118035901516, 21542506, 187027336, 12397847206, 28091779396, 17781586786, 14333296, 2022978526, 423531970577, 89579567, 70723031117, 1097349227, 7771023497, 155687, 77957, 484289537, 242844767, 121072637, 6726647, 3373277, 15885434898, 189112368, 47278158, 23118981228, 125712414858, 94485243048, 31428103878, 29549028, 11810655618, 34668, 14178, 5529619, 4877107249, 305366630479, 398131309, 34811596939, 55987369, 3041971399, 1555429, 760493059, 583549, 32779, 97609, 5839, 279249223700, 72529551410, 470292560, 73104353390, 80158740620, 40079370410, 52215529160, 8684081540, 8165090, 8030, 19400, 289085829141, 543598387251, 581865292881, 58137108591, 87123548301, 41659453611, 48269675721, 2631087591, 8204613381, 680011491, 330810801, 2922831, 1425981, 18853971, 9142101, 103431, 36141, 1088769392662, 78750351412, 572313682, 67648262512, 216449003662, 81869460652, 16375323082, 2396563432, 5419094662, 30404452, 16444492, 8694442, 141232, 83302, 3529718415383, 1386332651573, 660629053523, 260382781553, 188221501583, 61421691053, 28195154123, 4999657193, 5795608583, 88180133, 394243523, 207075233, 96578303, 51192413, 26503643, 5374553, 2901383, 1436804352024, 558627840054, 757446336084, 359936352114, 40808448144, 31649832174, 15377796204, 4296240234, 3151224264, 878688294, 349677324, 246807354, 85050384, 35059914, 19258194, 4743474, 3436254, 3383358750745, 2005844705335, 42065187925, 308833274995, 87485598865, 62886171055, 63556721485, 7648318315, 10469684425, 853688455, 142281685, 192572995, 121137505, 43117255, 17852305, 6683515, 2670445, 4339060254746, 16661790776, 332160860246, 408689763956, 45954293906, 33417593456, 6416949806, 8005469996, 1801388426, 538527176, 450347366, 334436396, 147885326, 35036156, 24983276, 8233316, 4644236, 1461467750427, 189789143097, 320007905367, 161642234997, 169531730067, 112532233137, 49385911887, 7505084397, 17271273867, 1646023977, 745718727, 28758597, 137667987, 26687217, 28796487, 7585677, 373467, 3658633021468, 720029260858, 753943058008, 133287897718, 121122708628, 43153948978, 56805209488, 23281033198, 10014632908, 6181064938, 1599105568, 1383561358, 559062388, 235103998, 85605838, 38482318, 15514348, 4678738329629, 2206667059259, 221126630489, 294349593719, 296358912149, 85417804979, 25035609809, 14517014639, 6160925069, 4110977099, 2403075929, 579312359, 649004789, 84418619, 108467549, 20482679, 21713909]); a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v := Explode([GPC.1, GPC.2, GPC.4, GPC.6, GPC.7, GPC.9, GPC.12, GPC.14, GPC.16, GPC.18, GPC.19, GPC.20, GPC.21, GPC.22, GPC.23, GPC.24, GPC.25, GPC.26, GPC.27, GPC.28, GPC.29, GPC.30]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "d", "e", "e2", "f", "f2", "f4", "g", "g2", "h", "h2", "i", "i2", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v"]); GPerm := PermutationGroup< 36 | (1,28,6,29,16,19,2,27,5,30,15,20)(3,35,13,23,12,34,9,21,8,26,18,31,4,36,14,24,11,33,10,22,7,25,17,32), (1,6,14,9,2,5,13,10)(3,18,12,16,4,17,11,15)(19,33,28,32)(20,34,27,31)(21,35,25,23,22,36,26,24), (1,33,2,34)(3,30,6,28,11,36,14,19,18,32,15,22,9,25,8,23)(4,29,5,27,12,35,13,20,17,31,16,21,10,26,7,24), (1,24,4,26)(2,23,3,25)(5,34,11,22)(6,33,12,21)(7,30,16,20)(8,29,15,19)(9,31,13,35,10,32,14,36)(17,28,18,27) >; /* Booleans */ RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable : BoolElt >; booleans_5435817984_t := 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>;