# Group 512.10494213 downloaded from the LMFDB on 29 December 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(0,512); a := GPC.1; b := GPC.2; c := GPC.3; d := GPC.4; e := GPC.5; f := GPC.6; g := GPC.7; h := GPC.8; i := GPC.9;
GPerm := Group( (1,2), (3,4), (5,6), (7,8), (9,10), (11,12), (13,14), (15,16), (17,18) );

 
# Booleans 
booleans_512_10494213 := rec( 
Agroup := true,
Zgroup := false,
abelian := true,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := true,
perfect := false,
quasisimple := false,
rational := true,
solvable := true,
supersolvable := true);