/* Group 3200000000.jlt downloaded from the LMFDB on 07 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([21, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 5, 2, 5, 2, 5, 5, 5, 5, 5, 42, 62671949110, 8724227654, 3687543617, 170, 90248751267, 25165217640, 271176258, 145905932764, 5813009185, 40008788026, 3124084597, 298, 317580806597, 174919967738, 6974707871, 25160035388, 4855777022, 181828274886, 219846374523, 36606883200, 11101838733, 11591984382, 11479331541, 426, 193384418311, 18187491868, 75105983281, 60383234758, 22465488283, 8957491984, 4119628954, 65821655600, 190913986397, 109146471890, 22337017991, 29159248196, 17732743673, 6587186894, 588168533, 1331316176, 463848740889, 318144059550, 1489857651, 30893486472, 1142092653, 4717718994, 1395543375, 2022720996, 1479243957, 618, 455448913930, 173978466847, 94565619508, 80014556233, 16646843230, 9010870291, 4531776616, 3063986005, 2672211874, 329296891403, 161426151968, 181156840757, 73544615498, 13486600607, 21703570676, 9835362569, 2439773438, 2672213219, 184486880, 728785481, 746, 546248521740, 59852083233, 161315481654, 76247912907, 6174604896, 13497382197, 7460552874, 6693981999, 3341531100, 458662041, 773189179405, 34346594722, 125409458551, 101457753676, 12158186641, 10218499318, 10504267339, 3045957760, 2094514981, 156437602, 147602923, 138500704, 874, 113223075854, 54842135075, 129443328056, 95360832077, 12580323938, 15576624119, 4208904140, 7724052161, 3855726182, 3213203, 52630445, 1042727263887, 274976701476, 130163335737, 35990169678, 48281904483, 30196992120, 15394848141, 4662336162, 477792183, 716016204, 499128225, 83294646, 28073067, 3222528, 253989, 1002, 36703027216, 433198080037, 260375899450, 11424000079, 342720100, 22848121, 2142000142, 11424163, 285847, 28849, 935940870161, 96768000038, 291755520059, 114670080080, 96768101, 120960122, 9253440143, 60480164, 15120206, 15452, 534842735634, 416747928615, 233429683260, 154768588881, 66291481638, 29430240123, 5173593744, 2745120165, 1380540186, 35910207, 242592249, 80133, 326860800019, 2150400040, 166119475261, 161280082, 63705600103, 3360000124, 20160145, 1680000166, 42000250, 4200292, 420334, 947875267604, 157152135209, 169912995902, 170038310483, 5503736552, 28365120125, 5590468946, 3157560167, 568890209, 220941251, 7717793, 2205335]); a,b,c,d,e,f,g,h,i,j,k,l,m := Explode([GPC.1, GPC.3, GPC.5, GPC.7, GPC.9, GPC.10, GPC.12, GPC.14, GPC.16, GPC.18, GPC.19, GPC.20, GPC.21]); AssignNames(~GPC, ["a", "a2", "b", "b2", "c", "c2", "d", "d2", "e", "f", "f2", "g", "g2", "h", "h2", "i", "i2", "j", "k", "l", "m"]);
GPerm := PermutationGroup< 40 | (1,35,36,19,3,34,38,20,4,31,39,18,2,32,37,17)(5,33,40,16)(6,28,14,21,8,29,12,24,9,27,11,23,7,26,13,25)(10,30,15,22), (1,19,14,26,2,17,12,28,3,20,15,30,4,18,13,27,5,16,11,29)(6,31,39,24,7,34,40,21,8,32,36,23,9,35,37,25,10,33,38,22), (1,23,40,29,3,25,38,26,4,21,37,27,2,24,39,30)(5,22,36,28)(6,17,13,34,9,19,15,33,8,20,11,35,10,18,14,31)(7,16,12,32) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_3200000000_jlt := 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>;