#= Group 113460.a downloaded from the LMFDB on 16 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(62, (1,62,2)(3,32,61)(4,14,59)(5,50,60)(6,28,29)(7,18,11)(8,21,47)(9,27,25)(10,41,15)(12,44,24)(13,33,38)(16,22,30)(17,43,56)(20,52,40)(23,54,49)(26,31,51)(34,42,48)(35,36,58)(37,55,39)(46,57,53), (3,39,14,6,7,20,47,28,17,25,42,24,34,57,50,4,11,22,52,16,55,21,35,56,12,46,36,5,27,32)(8,31,41,23,40,48,37,18,45,58,59,51,26,62,33,38,60,29,19,53,9,30,44,10,49,13,43,54,61,15))

 
#= Booleans =#
booleans_113460_a = (
    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,
)