#= Group 12180.a downloaded from the LMFDB on 06 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(30, (1,2,3)(4,5,7)(6,9,14)(8,12,19)(10,16,24)(11,13,20)(15,22,18)(17,25,26)(21,23,27)(28,30,29), (2,4,6,10,17,19,26,29,24,22,16,25,20,27)(5,8,13,9,15,23,12,14,21,28,30,7,11,18))

 
#= Booleans =#
booleans_12180_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,
)