/* Group 1600.5478 downloaded from the LMFDB on 15 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([8, -2, -2, -2, -2, -5, -2, -2, -5, 16, 1058, 66, 91, 10581, 141, 166]); a,b,c := Explode([GPC.1, GPC.3, GPC.6]); AssignNames(~GPC, ["a", "a2", "b", "b2", "b4", "c", "c2", "c4"]);
GPerm := PermutationGroup< 22 | (2,4)(5,6,8,7)(9,10)(11,12), (1,2)(3,4)(5,7,8,6)(9,11)(10,12), (1,3)(2,4)(5,8)(6,7)(9,12,11,10), (1,3)(2,4), (9,11)(10,12), (5,8)(6,7), (13,17,16,15,14), (18,22,21,20,19) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_1600_5478 := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := true,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true>;