# Group 78732.fx downloaded from the LMFDB on 24 October 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 
GPC := PcGroupCode(57449706449530738645401602738726575991066721086855450475003358948585159821749776309180116567843821050961818572637294983378490824485010812321671935,78732); a := GPC.1; b := GPC.3; c := GPC.5; d := GPC.6; e := GPC.7; f := GPC.8; g := GPC.9; h := GPC.11;
GPerm := Group( (1,2,5)(4,9,7,13,11,17)(8,14,16,18,12,15)(20,22)(21,24,23,26,25,27), (1,4)(2,7)(3,8,6,12,10,16)(5,11)(9,13,17)(19,21,22,25,20,23)(24,26), (1,3,5,10,2,6)(4,8,7,12,11,16)(9,15,17,14,13,18)(19,20,22)(21,23,25)(24,27,26) );

 
# Booleans 
booleans_78732_fx := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true);