# Group 4096.brz downloaded from the LMFDB on 05 September 2026. 
 
## Various presentations of this group are stored in this file: 
#	 GPC is polycyclic presentation, GPerm is permutation group 
#	 GLZ, GLFp, GLZN, 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(1852786533622931975968697803114300731211474631494413990351146525611887406639258,4096); a := GPC.1; b := GPC.2; c := GPC.4; d := GPC.5; e := GPC.7; f := GPC.8; g := GPC.10; h := GPC.11; i := GPC.12;
GPerm := Group( (6,8)(14,16)(22,24)(30,31), (1,12)(4,9)(6,16)(8,14)(17,28)(20,25)(22,31)(24,30), (1,9)(2,11)(3,13)(4,12)(5,10)(6,16)(7,32)(8,14)(15,23)(17,25)(18,29)(19,27)(20,28)(21,26)(22,31)(24,30), (3,6,13,16)(5,8,10,14)(18,22,29,31)(21,24,26,30), (1,4)(2,32)(7,11)(9,12)(15,19)(17,20)(23,27)(25,28), (6,16)(8,14)(22,31)(24,30), (1,19,12,23)(2,17,7,28)(3,13)(4,15,9,27)(5,10)(6,16)(8,14)(11,25,32,20)(18,21)(22,24)(26,29)(30,31), (1,9)(3,18)(4,12)(5,21)(6,22)(8,24)(10,26)(13,29)(14,30)(15,19)(16,31)(17,28)(20,25)(23,27), (1,25)(2,15)(4,28)(6,16)(7,27)(8,14)(9,17)(11,23)(12,20)(18,21)(19,32)(22,30)(24,31)(26,29), (1,4)(6,8)(9,12)(14,16)(17,20)(22,24)(25,28)(30,31), (1,9)(2,11)(4,12)(7,32)(15,23)(17,25)(19,27)(20,28) );

 
# Booleans 
booleans_4096_brz := 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 := true,
solvable := true,
supersolvable := true);