# Group 117600.d downloaded from the LMFDB on 21 September 2025. 
 
## Various presentations of this group are stored in this file: 
#	 GPC is polycyclic presentation GPerm is permutation group 
#	 GLZ, GLFp, GLZA, GLZq, GLFq if they exist are matrix groups 
 
# Many characteristics of the group are stored as booleans in a record: 
#	 Agroup, Zgroup, abelian, almost_simple,cyclic, metabelian, 
#	 metacyclic, monomial, nilpotent, perfect, quasisimple, rational, 
#	 solvable, supersolvable 
 

 
# Constructions 
GPerm := Group( (2,4,7,13,5,9,15,25,10,20,31,41,6,11,21,26,12,8,17,34,23,18,16,32)(14,27,39,50,29,43,47,22,30,38,48,40,46,24,33,28,44,19,35,36,49,37,45,42), (1,2,3)(4,8,17)(6,10,12)(7,14,28)(9,19,36)(11,22,37)(13,24,27)(15,25,32)(16,33,43)(18,29,44)(20,39,47)(21,38,35)(26,42,50)(30,45,41)(31,40,49)(34,48,46), (2,5,10,6,12,23)(4,9,20,11,8,18)(7,15,31,21,17,16)(13,25,41,26,34,32)(14,29,30,46,44,49)(19,37,27,43,38,24)(22,40,28,36,42,50)(33,35,45,39,47,48), (1,3)(2,6)(4,9)(5,10)(7,16)(8,11)(12,23)(13,26)(14,30)(15,17)(18,20)(19,38)(21,31)(25,41)(28,42)(32,34)(33,47)(35,39)(37,43)(40,50)(46,49) );

 
# Booleans 
booleans_117600_d := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := false,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := false,
supersolvable := false);