#= Group 1285608.a downloaded from the LMFDB on 09 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(138, (1,71,2)(3,86,124)(4,7,10)(5,132,24)(6,41,116)(8,36,111)(9,128,20)(11,28,66)(12,81,13)(14,88,84)(15,49,50)(16,125,104)(17,56,129)(18,109,70)(19,133,76)(21,101,126)(22,127,60)(23,96,135)(25,130,92)(26,51,131)(27,136,48)(29,69,100)(30,35,113)(31,89,105)(32,114,78)(33,55,42)(34,61,65)(37,45,98)(38,120,74)(39,117,122)(40,77,57)(43,134,82)(44,85,94)(46,90,80)(47,63,121)(52,83,123)(53,59,79)(54,107,115)(58,67,108)(62,106,72)(64,138,68)(73,93,99)(75,112,95)(87,91,118)(97,119,110)(102,103,137), (3,123,111,7,76,71,85,95,92,77,124,28,14,102,22,16,118,59,66,94,11,34,51,83,44,52,54,117,116,29,50,121,96,41,109,79,72,68,128,86,37,35,81,103,129,26,67,132,43,120,131,105,78,40,19,57,6,80,27,133,136,137,126,33,99,53,110,48)(4,5,8,114,61,135,84,122,101,63,36,10,21,98,9,74,115,12,38,60,106,104,55,13,73,69,62,32,100,45,20,91,112,25,24,87,89,97,58,90,107,130,47,75,82,23,125,119,39,127,113,17,64,49,46,56,70,65,134,30,18,138,93,31,88,42,108,15))

 
#= Booleans =#
booleans_1285608_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,
)