# Group 4752.h 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(95912109259417760139608623166727838487080807171684600119001,4752); a := GPC.1; b := GPC.2; c := GPC.6;
GPerm := Group( (1,2)(3,5)(4,7)(6,8)(9,10,11,12,13,14,15,16,17)(18,19,21,25,24,28,27,20,23,26,22), (2,4)(3,6)(19,22)(20,24)(21,26)(23,25)(27,28)(30,31), (1,3,7,6)(2,5,4,8)(18,20,25,22,27,21,26,28,19,23,24)(29,30,31) );
GLFp := Group([[[ Z(397)^2, 0*Z(397) ], [ 0*Z(397), Z(397)^20 ]], [[ Z(397)^3, 0*Z(397) ], [ 0*Z(397), Z(397)^393 ]], [[ 0*Z(397), Z(397)^0 ], [ Z(397)^0, 0*Z(397) ]]]);

 
# Booleans 
booleans_4752_h := 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);