/* Group 50000000.fd downloaded from the LMFDB on 30 September 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([15, -2, -2, -2, -2, -2, -2, -2, -5, 5, 5, 5, 5, 5, 5, 5, 30, 76, 407797232, 2595007203, 1187942658, 432109593, 109195728, 114001204, 1056447019, 419532334, 13335499, 214, 1865378885, 1082777780, 273537395, 158280170, 260, 3542642886, 1681092021, 1268556276, 447015291, 720092167, 483018262, 11557, 316805812, 30503107, 1042, 1057, 1080051848, 4492823, 64838, 212749253, 280868, 5483, 5498, 3769516809, 295209624, 360039, 165314454, 61350069, 37775484, 30099, 330190090, 1478425, 1980040, 861466375, 521470, 165085, 165100, 4531783691, 3314085146, 10800041, 229538936, 283608071, 35190806, 900101, 6929769612, 2655157467, 58500042, 621619497, 472875072, 31981647, 4875102, 1683978253, 426733468, 315000043, 303660058, 26675113, 26250088, 26250103, 2055110414, 3245428829, 1687500044, 1063407659, 438750074, 239062589, 140625104]); a,b,c,d,e,f,g,h,i,j,k := Explode([GPC.1, GPC.4, GPC.5, GPC.8, GPC.9, GPC.10, GPC.11, GPC.12, GPC.13, GPC.14, GPC.15]); AssignNames(~GPC, ["a", "a2", "a4", "b", "c", "c2", "c4", "d", "e", "f", "g", "h", "i", "j", "k"]);
GPerm := PermutationGroup< 40 | (1,22)(2,23,3,24,5,21,4,25)(6,28,7,29,9,26,8,30)(10,27)(11,32)(12,33,13,34,15,31,14,35)(16,39,19,40,20,37,17,36)(18,38), (1,11,4,12,3,15,5,14)(2,13)(6,36,7,40,10,37,9,38)(8,39)(16,27)(17,26,18,30,20,28,19,29)(21,33)(22,32,23,31,25,34,24,35), (1,9,13,39)(2,6,11,36,4,10,12,40,5,7,15,37,3,8,14,38)(16,24,29,32)(17,25,27,35,19,22,28,31,20,23,26,34,18,21,30,33) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_50000000_fd := 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>;