/* Group 300696.a downloaded from the LMFDB on 13 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< 136 | (1,3,4)(2,5,6)(7,12,13)(8,14,16)(9,18,19)(10,20,22)(11,23,24)(15,29,30)(17,33,34)(21,39,40)(25,48,49)(26,50,52)(27,53,55)(28,57,45)(31,62,63)(32,64,66)(35,72,73)(36,74,75)(37,76,78)(38,80,69)(41,84,85)(42,86,88)(43,90,91)(44,65,93)(46,95,96)(47,59,97)(51,102,103)(54,92,105)(56,109,107)(58,110,111)(60,106,112)(61,113,114)(67,120,121)(68,87,99)(70,123,94)(71,82,117)(77,122,125)(79,129,127)(81,104,130)(83,126,131)(89,118,133)(98,108,135)(100,128,136)(116,134,119), (1,2)(3,7,11,20,38,79,128,83,40,82,127,78,126,93,72,100,49,86,118,66,117,91,57,92,44,23,43,89,54,27,13,21,10,5,9,17,14,28,56,108,60,30,59,107,55,106,99,48,98,73,64,116,88,97,121,80,122,68,33,67,119,77,37,19,15,8)(4,6)(12,25,47,46,24,45,94,52,63,115,135,130,112,125,103,113,129,90,123,133,101,50,62,104,53,29,58,65,32,16,31,61,36,18,35,71,70,34,69,96,75,85,132,136,111,131,105,114,102,109,120,95,134,124,74,84,110,76,39,81,87,42,22,41,51,26) >;
GLFp := MatrixGroup< 2, GF(67) | [[1, 1, 0, 1], [1, 0, 1, 1]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_300696_a := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := false,
nilpotent := false,
perfect := true,
quasisimple := true,
rational := false,
solvable := false,
supersolvable := false>;