# Group 9240.a downloaded from the LMFDB on 04 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(38899698737788854599812578737067875291784826860001359,9240); a := GPC.1; b := GPC.2;
GPerm := Group( (1,2,3,5,7,6,4)(8,9,10,11,12,13,14,15,16,17,18)(19,20,22,21)(23,24,25)(26,27,28,30,29), (2,4)(3,6)(5,7)(19,21)(20,22)(24,25)(27,29)(28,30) );
GLFp := Group([[[ Z(419)^0, 0*Z(419) ], [ 0*Z(419), Z(419)^209 ]], [[ Z(419)^344, Z(419)^227 ], [ Z(419)^226, Z(419)^344 ]]]);

 
# Booleans 
booleans_9240_a := 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);