/* Group 8264970432.v 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, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 147121676352, 100535522549, 169422354384, 49834072172, 66721582834, 186, 299134251555, 226744448834, 11560973256, 173563459744, 276261004602, 79212726620, 24218106178, 326, 450125292245, 58510108324, 28172423499, 2910066518, 6946753278, 826605106494, 60631608269, 119563719208, 369567525, 20895770210, 10382769532, 466, 1499936811271, 647242406814, 185005630709, 57477223084, 19262411043, 9463882250, 974833648280, 55145083207, 119860986114, 52653499601, 25111142362, 8743852761, 7093222364, 9263626, 606, 810968967369, 224590230752, 198059272615, 1609979838, 13894800581, 14987479084, 4992249507, 6070790, 668452805866, 819117423861, 318647761004, 38840464951, 11473620942, 6488001953, 111764416, 33203385, 374307116, 5992522, 746, 713466164747, 3302964898, 1413614649, 522593936, 46685766631, 87277950, 79637, 4839027, 1220690, 3408485196, 549349695683, 1527540826, 568080945, 30519427640, 94292767, 129318, 5260204, 1309839, 241288129165, 472207562100, 397132646459, 194223264562, 37437059625, 28203266576, 2757110983, 20448462, 689983085, 601072, 79260543, 52476, 644657616014, 805430790037, 220994425500, 1641824723, 8977722586, 275649609, 127429352, 45606415, 21238398, 7601261, 37504, 14951923, 2704490809359, 471454774310, 162019118653, 225335603028, 953963, 37562372482, 1043757127, 3088928877712, 916597758711, 250466429726, 1231368565, 76052965932, 348887867, 179384698, 54727665, 26477156, 9121471, 950376, 16923186, 2520509871761, 789792831, 29726683885, 2667511123794, 4957845449, 925419232, 95373110535, 31709482238, 15620271469, 5097416, 2725909, 303227, 587386909459, 1405695202602, 200922612545, 138251292568, 80583410991, 45359429894, 222665917, 109991700, 96578123, 9389769, 12407898, 2943881, 1378984, 327447, 2374744817108, 237915413611, 651415059858, 73384732601, 56826279328, 28971364095, 6905992118, 348820849, 2583370140, 62127551, 194441560, 13760023, 6299145, 1526162, 701704, 19294, 3747570976533, 420268476716, 527741419459, 233010328410, 85267274513, 45209197576, 4327138095, 1098261038, 1078751725, 185256948, 120417119, 3418856, 126383, 27782, 9589, 1356543122134, 215687468781, 394671741044, 284232842731, 88637555778, 40624965641, 11315221288, 3379243719, 385983998, 567835177, 313997724, 10442781, 387618, 33786, 11591]); a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r := Explode([GPC.1, GPC.2, GPC.3, GPC.5, GPC.7, GPC.9, GPC.11, GPC.13, GPC.14, GPC.15, GPC.16, GPC.17, GPC.18, GPC.19, GPC.20, GPC.21, GPC.22, GPC.23]); AssignNames(~GPC, ["a", "b", "c", "c2", "d", "d2", "e", "e2", "f", "f2", "g", "g2", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r"]);
GPerm := PermutationGroup< 36 | (1,22,20,17,2,23,19,16,3,24,21,18)(4,13,35,9,29,25,10,32,5,14,34,8,28,26,11,31,6,15,36,7,30,27,12,33), (1,26,3,25,2,27)(4,7,29,33,16,19,6,8,30,31,18,21,5,9,28,32,17,20)(10,35,22)(11,36,24,12,34,23)(13,14), (1,23,2,24,3,22)(4,29,18,5,30,16)(6,28,17)(7,33,19,8,32,21)(9,31,20)(10,15,35,26,11,13,34,27,12,14,36,25) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_8264970432_v := 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>;