# Group 19600.c downloaded from the LMFDB on 15 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(47333245561223889388778954268441653127923681255316813535885367735,19600); a := GPC.1; b := GPC.4;
GPerm := Group( (14,16)(15,17)(19,21)(24,25)(27,29)(28,31)(30,32), (1,2,3,4,5,6,7)(8,9,10,11,12)(13,14,15,17,16)(18,19,22,24,20,21,23,25)(26,27,28,30,32,31,29), (13,15,16,14,17)(18,20)(19,21)(22,23)(24,25)(26,28,32,29,27,30,31) );
GLFp := Group([[[ Z(281)^3, 0*Z(281) ], [ 0*Z(281), Z(281)^279 ]], [[ Z(281)^4, 0*Z(281) ], [ 0*Z(281), Z(281)^276 ]], [[ 0*Z(281), Z(281)^0 ], [ Z(281)^0, 0*Z(281) ]]]);

 
# Booleans 
booleans_19600_c := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := true,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true);