/* Group 1600.5495 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, -2, -5, -2, -5, 41, 66, 16332, 116, 166]); a,b,c,d := Explode([GPC.1, GPC.2, GPC.5, GPC.7]); AssignNames(~GPC, ["a", "b", "b2", "b4", "c", "c2", "d", "d2"]);
GPerm := PermutationGroup< 24 | (1,2,4,6,3,5,7,8)(12,14), (1,3)(2,5)(4,7)(6,8)(9,10)(11,12)(13,14), (1,3)(2,5)(4,7)(6,8)(9,10), (11,13)(12,14), (1,4,3,7)(2,6,5,8), (1,3)(2,5)(4,7)(6,8), (15,19,18,17,16), (20,24,23,22,21) >;
GLZN := MatrixGroup< 2, Integers(88) | [[9, 0, 0, 1], [43, 0, 44, 43], [45, 0, 0, 45], [65, 55, 66, 65], [1, 0, 0, 65], [9, 0, 0, 9], [23, 22, 44, 23], [1, 44, 0, 1]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_1600_5495 := 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>;