/* Group 976500.a downloaded from the LMFDB on 24 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< 126 | (3,58,40,62,43,125,92,20,85,118,70,91,87,19,7,10,107,60,104,24,75,29,14,6,98,84,33,78,57,106,79,21,34,101,17,81,83,80,64,114,82,77,12,53,13,32,8,68,93,120,124,102,66,90,41,103,94,99,16,111,55,56)(4,86,67,89,71,126,73,74,18,113,30,35,26,88,39,63,27,5,9,36,61,121,97,116,76,117,52,47,15,65,49,46,48,112,28,95,108,50,23,72,51,96,45,31,123,115,100,54,105,25,69,22,119,122,110,42,38,59,11,44,109,37), (1,51,2)(3,41,18)(4,60,32)(5,123,15)(6,94,115)(7,53,126)(8,34,100)(9,85,83)(10,84,97)(11,57,64)(12,91,113)(13,63,62)(14,73,17)(16,87,110)(19,81,39)(20,28,29)(21,24,26)(22,33,68)(23,61,46)(25,109,45)(27,69,116)(30,56,90)(31,42,122)(35,36,44)(37,74,121)(38,40,43)(47,117,50)(48,80,103)(49,67,59)(52,77,99)(54,93,106)(55,107,105)(58,75,96)(65,92,78)(66,72,101)(70,114,88)(71,104,82)(76,120,102)(79,95,111)(86,119,108)(89,118,124)(98,125,112) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_976500_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>;