/* Group 174182400.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 
 
 The character table is stored as chartbl_n_i where n is the order of 
 the group and i is which group of that order it is. Conjugacy classes 
 are stored in the variable 'C' with elements from the group 'G'. 
*/
 
/* Constructions */
GPerm := PermutationGroup< 120 | (2,3,5,9)(4,7)(6,11)(8,14,18,30)(10,17,28,45)(12,20,27,38)(13,22,37,57)(15,24,40,61)(16,26,43,66)(19,32,29,47)(21,35)(23,39,60,78)(25,42)(31,50,73,97)(33,53)(34,51)(36,55)(41,63,44,48)(46,70,93,109)(49,69,92,76)(52,75)(54,56,65,74)(58,80,101,115)(59,82,62,85)(67,91,98,84)(68,83)(71,95,110,104)(72,87,103,105)(79,100,89,107)(81,102,94,90)(88,99,114,108)(96,111,119,116)(106,118,120,117)(112,113), (1,2,4,8,15,25)(3,6,12,21,36,39)(5,10,18,31,51,74)(7,13,23,32,52,76)(9,16,27,44,68,80)(11,19,33,54,78,99)(14,20,34,55,79,100)(17,29,48,72,96,50)(22,38,59,83,104,107)(24,41,64,88,35,56)(26,37,58,81,57,47)(28,46,71,91,43,67)(30,49,42,65,89,101)(40,62,86,97,112,102)(45,69)(53,77,61)(60,84,75,98,113,93)(63,87,106,118,119,114)(66,90,108)(70,94)(73,85,105,117,111,115)(82,103,116,95,110,92) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_174182400_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 := true,
solvable := false,
supersolvable := false>; 

 
/* Character Table */

 /* Character tables not currently available for download for groups of Lie type. */