/* Group 31416.c downloaded from the LMFDB on 27 October 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([7, -2, -2, -2, -3, -7, -11, -17, 209132, 8597, 36, 25790, 58, 68771, 108, 257884, 277, 846725, 502]); a,b := Explode([GPC.1, GPC.2]); AssignNames(~GPC, ["a", "b", "b2", "b4", "b12", "b84", "b924"]);
GPerm := PermutationGroup< 46 | (1,2,4,7)(3,6,8,5)(9,10,11)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39)(41,42)(43,44)(45,46), (1,3,4,8)(2,5,7,6)(9,10,11)(12,13,15,17,19,21,22,20,18,16,14)(23,25,27,29,31,33,35,37,39,24,26,28,30,32,34,36,38)(40,41,43,45,46,44,42) >;
GLFp := MatrixGroup< 2, GF(307) | [[69, 285, 57, 69], [162, 181, 148, 145]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_31416_c := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := true,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true>;