# Group 17640.i downloaded from the LMFDB on 26 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(14854128979258037214324412215518032083873577718396966710644452699,17640); a := GPC.1; b := GPC.4;
GPerm := Group( (1,2,3,5,4)(6,7,8)(16,17,19,22)(18,21,23,20)(27,28,30,33,29,32,31), (2,4)(3,5)(7,8)(9,10,11,12,13,14,15)(16,18,19,23)(17,20,22,21)(24,25,26)(28,31)(29,33)(30,32), (6,8,7)(9,11,13,15,10,12,14)(24,26,25)(27,29,28,32,30,31,33) );
GLFp := Group([[[ Z(421), 0*Z(421) ], [ 0*Z(421), Z(421)^419 ]], [[ Z(421)^0, 0*Z(421) ], [ 0*Z(421), Z(421)^20 ]], [[ 0*Z(421), Z(421)^10 ], [ Z(421)^0, 0*Z(421) ]]]);

 
# Booleans 
booleans_17640_i := 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);