/* Group 1093750.c downloaded from the LMFDB on 15 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([9, -2, -5, -7, -5, 5, 5, 5, 5, 5, 8081640, 12447505, 100, 16622282, 21709803, 11055252, 2403849, 20303338, 177682, 58359425, 26255894, 2062391, 28065246, 32087175, 4727544, 77253127, 38986936, 2668705, 57958748, 24491582, 5080913]); a,b,c,d,e,f,g,h := Explode([GPC.1, GPC.2, GPC.4, GPC.5, GPC.6, GPC.7, GPC.8, GPC.9]); AssignNames(~GPC, ["a", "b", "b5", "c", "d", "e", "f", "g", "h"]);
GPerm := PermutationGroup< 35 | (1,3)(4,5)(6,34,9,31,7,33,10,35,8,32)(11,27,14,29,12,26,15,28,13,30)(16,24,20,23,19,22,18,21,17,25), (1,13,2,12,3,11,4,15,5,14)(6,9)(7,8)(16,31,17,35,18,34,19,33,20,32)(21,30,25,26,24,27,23,28,22,29) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_1093750_c := rec< RF |  
Agroup := true,
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>;