/* Group 1720.4 downloaded from the LMFDB on 05 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([5, -2, -2, -2, -5, -43, 10, 26, 42, 118]); a := Explode([GPC.1]); AssignNames(~GPC, ["a", "a2", "a4", "a8", "a40"]);
GPerm := PermutationGroup< 56 | (1,8,4,6,2,7,3,5), (1,4,2,3)(5,8,6,7), (1,2)(3,4)(5,6)(7,8), (9,13,12,11,10), (14,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15) >;
GLFp := MatrixGroup< 2, GF(431) | [[25, 351, 358, 25]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_1720_4 := rec< RF |  
Agroup := true,
Zgroup := true,
abelian := true,
almost_simple := false,
cyclic := true,
metabelian := true,
metacyclic := true,
monomial := true,
nilpotent := true,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true>;