# Group 1728.825 downloaded from the LMFDB on 12 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(44788237216123066334736466421247716485639,1728); a := GPC.1; b := GPC.3; c := GPC.5;
GPerm := Group( (1,2)(3,5)(4,6)(7,8)(9,10,11,12)(13,14,17,16)(15,19,20,18), (1,3,4,7)(2,5,6,8)(9,11)(10,12)(13,15,17,20)(14,18,16,19), (2,6)(5,8)(13,16,17,14)(15,19,20,18), (13,17)(14,16)(15,20)(18,19), (1,4)(2,6)(3,7)(5,8), (9,11)(10,12)(13,17)(14,16)(15,20)(18,19), (21,47,38,29,44,35,26,41,32,23,46,37,28,43,34,25,40,31,22,45,36,27,42,33,24,39,30), (21,29,26,23,28,25,22,27,24)(30,38,35,32,37,34,31,36,33)(39,47,44,41,46,43,40,45,42), (21,23,22)(24,26,25)(27,29,28)(30,32,31)(33,35,34)(36,38,37)(39,41,40)(42,44,43)(45,47,46) );

 
# Booleans 
booleans_1728_825 := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := true,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true);