/* Group 688747536.dq 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([20, 2, 3, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 11208460800, 5017283201, 13528056501, 22375386002, 12960155362, 5859196602, 21901240803, 10479164423, 7255622283, 223, 5427453604, 26111048424, 7508944444, 284, 76039032965, 32286435865, 6124768365, 77381082246, 45348740666, 15451615246, 2640635826, 2199121766, 55354890247, 32309740827, 14539641647, 5685083587, 3261260247, 1573591787, 8748607, 85844387528, 53684523388, 9795556848, 1793700788, 2743107208, 999945108, 782218748, 63598648, 14748, 42862051209, 37814952029, 8833488049, 8089526469, 2646406889, 977605309, 96670929, 41749349, 11635969, 3353589, 111344777290, 10175790270, 14762230610, 11120107750, 390899610, 11553450, 518930, 642370, 52844958731, 24485385631, 9162138291, 1519542791, 5835469051, 2451947871, 287362211, 45450871, 1713791, 236371, 951, 1842328832, 122821972, 982575432, 99532245133, 49881417633, 285398453, 13247841673, 6094396653, 3805817513, 645631693, 113831073, 68040173, 1406353, 75813, 1182113, 2793, 100311638414, 91207742434, 13369464054, 9446868074, 6616315894, 4081598214, 693060434, 126335854, 73702074, 243194, 97414, 1174734, 60574, 1194, 14511882255, 16796195, 5598775, 377913675, 8673117136, 499685796, 2575761176, 3061100177, 8673117157, 88179917, 158366793618, 79726356038, 30079201018, 17014199118, 2784051098, 97234178, 23269858, 14128218, 1077538, 143918, 48178, 113374080019, 121058323239, 13716864059, 19990929679, 8030664099, 225698559, 25660999, 2786639]); a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p := Explode([GPC.1, GPC.2, GPC.3, GPC.4, GPC.7, GPC.8, GPC.9, GPC.10, GPC.11, GPC.12, GPC.14, GPC.15, GPC.17, GPC.18, GPC.19, GPC.20]); AssignNames(~GPC, ["a", "b", "c", "d", "d2", "d4", "e", "f", "g", "h", "i", "j", "j3", "k", "l", "l3", "m", "n", "o", "p"]);
GPerm := PermutationGroup< 36 | (1,10,31,27,24,8,14,35,19)(2,12,33,25,23,7,15,34,21)(3,11,32,26,22,9,13,36,20)(4,28,18)(5,29,16)(6,30,17), (1,27)(2,25)(3,26)(4,35,29,24,16,12,5,34,30,23,17,11,6,36,28,22,18,10)(7,20,32,8,21,33,9,19,31) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_688747536_dq := 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>;