#= Group 1092.25 downloaded from the LMFDB on 08 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(14, (2,3,5,9,6,11,8,13,10,7,12,14,4), (3,6,9,4,7,12)(5,10,8,14,11,13), (1,2)(3,4)(5,8)(6,9)(7,12)(13,14))
GLFp = matrix_group([matrix(GF(13), [[11, 5, 8], [0, 8, 11], [1, 3, 10]]), matrix(GF(13), [[4, 0, 9], [6, 12, 3], [7, 0, 9]])])

 
#= Booleans =#
booleans_1092_25 = (
    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,
)