/* Group 8264970432.i downloaded from the LMFDB on 24 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([23, 3, 2, 2, 2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 92614476096, 174403512247, 94618612216, 307842792959, 90844532971, 20944658592, 280459657131, 188504770090, 118980034681, 256, 63342930124, 21919262227, 27917249630, 17674943496, 457858279013, 144377324476, 173912154051, 23688259250, 12409270597, 396, 1136358304038, 95488322077, 11298895044, 77791602691, 36385643322, 577316078479, 455666900126, 233974424341, 70209715436, 38379308163, 28706145194, 9479418313, 536, 1313770192136, 175598504095, 244417969206, 84150211397, 37488741724, 10448928735, 1101771509769, 305831066272, 315436491895, 35397487678, 39013924901, 33973764724, 13764481707, 374663270, 1222669153, 731879766, 2019699437194, 272625772705, 24326035064, 144288221607, 32915917422, 32271863441, 12988682140, 7171715271, 1344773624, 135691960, 91112118, 1458179698187, 426628152610, 69711770937, 184192137296, 84709745671, 22230001710, 20404544909, 2934433828, 1764007827, 736491314, 438451909, 100899324876, 666520734499, 221607519386, 33543066313, 9944759240, 38468412031, 17893966110, 2841489863, 1589493166, 624648594, 210148505, 125414320, 11794941, 1708204538893, 729788301348, 42684474619, 7752946066, 66030280953, 1957100672, 15122761063, 1457974314, 2039064875, 661283248, 284308533, 73338020, 47157511, 13745526, 1177717060814, 869396113957, 116462450460, 127781914283, 82580886466, 21132812289, 17832375332, 3278195005, 1548292923, 1548274316, 457549939, 165008247, 44072660, 19432438, 1512471, 314939086863, 8673188902, 28179061309, 74815574740, 116980272875, 24986584834, 15288284889, 10202748656, 2111360455, 135586878, 530499845, 5139388, 59149299, 5518106, 2147617, 1464, 1431835268560, 239870579943, 30168527845, 123136956, 1277544975, 2274873590033, 1078504948264, 2086083135, 157629652214, 391140685, 9892597246, 419863922514, 791739707369, 136522547776, 179204533575, 1238611934, 62515491361, 11882843873, 1519593435, 168843961, 56281524, 11185769, 6253810, 2084853, 1903550803219, 359985254442, 450535996865, 79855632088, 112199398671, 65009012534, 3852460620, 32192866, 179183612, 1192615, 19996518, 132821, 2215264, 148279299860, 1170722911723, 659591245218, 49319392841, 113854502776, 56851196355, 6662647081, 1365823280, 202461775, 38145198, 50586335, 10511365, 5621013, 821948, 3484106410773, 309783336236, 155529082435, 38882270682, 38722917137, 12097591886, 2843081197654, 272042473581, 633446708036, 301746086011, 19825032642, 55518421061, 7600984293, 1414917058, 471639195, 249767096, 52404625, 24224289, 5823047, 3456853]); a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s := Explode([GPC.1, GPC.2, GPC.3, GPC.4, GPC.6, GPC.8, GPC.10, GPC.11, GPC.12, GPC.13, GPC.14, GPC.15, GPC.16, GPC.18, GPC.19, GPC.20, GPC.21, GPC.22, GPC.23]); AssignNames(~GPC, ["a", "b", "c", "d", "d2", "e", "e2", "f", "f2", "g", "h", "i", "j", "k", "l", "m", "m3", "n", "o", "p", "q", "r", "s"]);
GPerm := PermutationGroup< 36 | (1,5,9,13,30,20,25,16,31,3,4,8,14,28,21,27,18,33)(2,6,7,15,29,19,26,17,32)(10,22,34)(11,24,35,12,23,36), (1,35,20,13,10,8,25,22,31,2,34,19,14,12,7,26,24,33,3,36,21,15,11,9,27,23,32)(4,6,5)(16,18,17), (1,11,14,24,3,12,13,22,2,10,15,23)(4,8,16,21,6,9,18,19,5,7,17,20)(25,35,26,34,27,36)(28,31,29,33,30,32) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_8264970432_i := 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>;