# Group 3168.c downloaded from the LMFDB on 21 November 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(3976166881536833915045964957510993751887459000011900,3168); a := GPC.1; b := GPC.2; c := GPC.7;
GPerm := Group( (2,4)(3,5)(6,9)(7,8)(10,11)(21,22)(23,25)(24,27)(26,28), (1,2,5,8,9,10,11,6,7,3,4)(12,13,14,15,16,17,18,19,20)(21,23,26,24), (1,3,6,10,8,2,4,7,11,9,5)(21,24,26,23)(22,25,28,27) );
GLFp := Group([[[ Z(397), 0*Z(397) ], [ 0*Z(397), Z(397)^10 ]], [[ Z(397)^9, 0*Z(397) ], [ 0*Z(397), Z(397)^387 ]], [[ 0*Z(397), Z(397)^0 ], [ Z(397)^0, 0*Z(397) ]]]);

 
# Booleans 
booleans_3168_c := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true);