# Group 16384.cw downloaded from the LMFDB on 06 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(285343994728385976596876783738663529795946882732611442963509245618610511848627084633539921935432875752139612281406532501890938016977875230947522860291891277924517400888576224058656663392984063,16384); a := GPC.1; b := GPC.3; c := GPC.4; d := GPC.7; e := GPC.9; f := GPC.12;
GLZq := Group([[[ZmodnZObj(9,32), ZmodnZObj(0,32)], [ZmodnZObj(0,32), ZmodnZObj(1,32)]],[[ZmodnZObj(1,32), ZmodnZObj(8,32)], [ZmodnZObj(0,32), ZmodnZObj(1,32)]],[[ZmodnZObj(17,32), ZmodnZObj(0,32)], [ZmodnZObj(0,32), ZmodnZObj(1,32)]],[[ZmodnZObj(3,32), ZmodnZObj(0,32)], [ZmodnZObj(0,32), ZmodnZObj(3,32)]],[[ZmodnZObj(19,32), ZmodnZObj(26,32)], [ZmodnZObj(10,32), ZmodnZObj(9,32)]],[[ZmodnZObj(1,32), ZmodnZObj(4,32)], [ZmodnZObj(0,32), ZmodnZObj(1,32)]],[[ZmodnZObj(9,32), ZmodnZObj(0,32)], [ZmodnZObj(0,32), ZmodnZObj(9,32)]],[[ZmodnZObj(11,32), ZmodnZObj(9,32)], [ZmodnZObj(2,32), ZmodnZObj(9,32)]],[[ZmodnZObj(1,32), ZmodnZObj(16,32)], [ZmodnZObj(0,32), ZmodnZObj(1,32)]],[[ZmodnZObj(1,32), ZmodnZObj(2,32)], [ZmodnZObj(0,32), ZmodnZObj(1,32)]],[[ZmodnZObj(17,32), ZmodnZObj(0,32)], [ZmodnZObj(0,32), ZmodnZObj(17,32)]],[[ZmodnZObj(1,32), ZmodnZObj(16,32)], [ZmodnZObj(16,32), ZmodnZObj(17,32)]],[[ZmodnZObj(13,32), ZmodnZObj(24,32)], [ZmodnZObj(24,32), ZmodnZObj(21,32)]],[[ZmodnZObj(1,32), ZmodnZObj(24,32)], [ZmodnZObj(8,32), ZmodnZObj(25,32)]]]);

 
# Booleans 
booleans_16384_cw := 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);