/* Group 194472.a downloaded from the LMFDB on 14 October 2026. */
 
/* Various presentations of this group are stored in this file: 
	 GPC is polycyclic presentation, GPerm is permutation group 
	 GLZ, GLFp, GLZN, 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 */
GPerm := PermutationGroup< 74 | (3,67,43,70,39,31,50,9,47,29,51,12,52,45,23,57,42,71,60,44,16,14,11,24,40,58,5,15,21,41,28,64,18,55,4,8)(6,35,20,54,32,25,65,26,48,30,68,27,46,38,7,34,10,74,69,73,22,59,13,49,36,56,62,72,19,37,53,66,63,61,33,17), (1,7,2)(3,50,66)(4,20,67)(5,71,53)(6,38,27)(8,31,61)(9,39,62)(10,45,47)(11,54,52)(12,58,35)(13,30,37)(14,29,26)(15,24,49)(16,59,18)(17,73,65)(19,74,34)(21,46,55)(23,25,60)(28,72,42)(32,64,43)(33,40,57)(36,70,51)(41,56,44)(63,69,68) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable : BoolElt >; 
booleans_194472_a := rec< RF | 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := true,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := false,
nilpotent := false,
perfect := true,
quasisimple := true,
rational := false,
solvable := false,
supersolvable := false>;