#= Group 194472.a downloaded from the LMFDB on 11 October 2026. =#
 
#= Various presentations of this group are stored in this file: 
	 GPC is polycyclic presentation, GPerm is permutation group 
	 GLZ, GLFp, GLZN, GLZq, GLFq if they exist are matrix groups 
 
 Many characteristics of the group are stored as booleans in a NamedTuple: 
	 Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, 
	 metacyclic, monomial, nilpotent, perfect, quasisimple, rational, 
	 solvable, supersolvable 
 
=#
 
#= Constructions =#
GPerm = @permutation_group(74, (3,67,43,70,39,31,50,9,47,29,51,12,52,45,23,57,42,71,60,44,16,14,11,24,40,58,5,15,21,41,28,64,18,55,4,8)(6,35,20,54,32,25,65,26,48,30,68,27,46,38,7,34,10,74,69,73,22,59,13,49,36,56,62,72,19,37,53,66,63,61,33,17), (1,7,2)(3,50,66)(4,20,67)(5,71,53)(6,38,27)(8,31,61)(9,39,62)(10,45,47)(11,54,52)(12,58,35)(13,30,37)(14,29,26)(15,24,49)(16,59,18)(17,73,65)(19,74,34)(21,46,55)(23,25,60)(28,72,42)(32,64,43)(33,40,57)(36,70,51)(41,56,44)(63,69,68))

 
#= Booleans =#
booleans_194472_a = (
    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,
)