# 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 dict: 
#	 Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, 
#	 metacyclic, monomial, nilpotent, perfect, quasisimple, rational, 
#	 solvable, supersolvable 
 

 
# Constructions 
GPerm = PermutationGroup(['(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
}