/* Group 74412.a downloaded from the LMFDB on 15 September 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 */
GPerm := PermutationGroup< 54 | (3,28,40,36,34,22,37,53,25,27,10,9,14,41,6,46,26,15,7,24,19,49,18,12,5,13)(4,20,35,23,21,17,29,54,44,52,45,39,8,38,33,50,42,31,11,51,16,43,48,47,30,32), (1,29,2)(3,51,28)(4,49,13)(5,34,11)(6,33,7)(8,40,37)(9,14,47)(10,19,42)(12,36,16)(15,48,53)(17,18,24)(20,43,52)(21,32,35)(22,54,25)(23,31,39)(26,50,46)(27,30,41)(38,44,45) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_74412_a := rec< RF |  
Agroup := true,
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>;