/* Group 456288.a downloaded from the LMFDB on 22 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< 98 | (3,38,52,6,71,74,34,12,82,41,48,64,5,90,47,39,77,51,84,16,40,59,86,94,69,66,43,9,65,93,29,33,56,21,23,18,44,55,4,75,20,73,91,87,70,76,88,79)(7,15,42,61,85,17,50,24,62,54,11,96,37,53,60,19,89,67,27,30,95,49,63,98,22,13,25,31,14,10,28,81,26,97,46,57,83,78,80,45,68,72,8,36,92,58,35,32), (1,98,2)(3,21,53)(4,59,57)(5,82,25)(6,30,69)(7,65,84)(8,15,42)(9,60,74)(10,33,23)(11,17,28)(12,80,38)(13,51,71)(14,73,66)(16,35,93)(18,95,75)(20,88,62)(22,37,54)(24,55,52)(26,40,91)(27,86,34)(29,49,87)(31,70,94)(32,68,50)(36,39,44)(41,96,43)(45,76,48)(46,63,78)(47,79,97)(56,61,64)(58,85,92)(67,90,77)(72,83,89) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_456288_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>;