# Group 532400.d downloaded from the LMFDB on 18 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(22673277554578910327958770773966636166109735213676470366175635211791591261858981080127092713299504402370316398493708394231560281872847675654120495832803311229030900399,532400); a := GPC.1; b := GPC.3; c := GPC.5; d := GPC.9;
GPerm := Group( (20,21,22,23,24), (1,2,5,3,4,9,7,8,11,6,10)(20,22,24,21,23)(26,32,35,43,34,40,37,44,36,46,45), (2,7,3,8,6,10,9,11,4,5)(12,13,14,16)(15,19,18,17)(20,23,21,24,22)(25,26,33,34,28,40,41,36,27,37)(29,35,42,45,38,32,31,44,30,43)(39,46), (12,14)(13,16)(15,18)(17,19)(20,21,22,23,24), (1,3,7,6,2,4,8,10,5,9,11)(20,24,23,22,21)(25,27,38,31,29,41,30,39,33,42,28)(26,34,36,32,40,46,35,37,45,43,44), (1,4,9,11,7)(2,8,3,5,10)(12,15,14,18)(13,17,16,19)(20,23,21,24,22)(25,28,38,29,42,41,30,31,27,39)(26,35,44,43,34,32,45,40,46,36), (1,2,3,8,4,6,11,7,5,9)(12,14)(13,16)(15,18)(17,19)(20,21,22,23,24)(25,29,27,30,41,31,28,38,33,42)(26,34,32,37,40,43,45,35,36,46), (1,5,4,7,11,10,2,3,9,8,6)(12,14)(13,16)(15,18)(17,19)(20,23,21,24,22)(25,30,27,39,38,33,31,42,29,28,41)(26,34,36,32,40,46,35,37,45,43,44), (1,6,10,4,8)(2,3,5,11,9)(20,23,21,24,22)(25,31,39,41,30)(26,36,34,37,40)(27,33,28,42,29)(32,35,44,45,43) );
GLFp := Group([[[ Z(11), 0*Z(11), 0*Z(11), 0*Z(11) ], [ Z(11)^4, Z(11)^7, Z(11)^2, 0*Z(11) ], [ Z(11)^5, Z(11)^5, Z(11)^5, 0*Z(11) ], [ Z(11)^3, Z(11)^5, Z(11)^9, Z(11)^2 ]], [[ Z(11)^2, 0*Z(11), 0*Z(11), 0*Z(11) ], [ Z(11)^4, Z(11)^6, Z(11)^2, 0*Z(11) ], [ Z(11), Z(11), Z(11)^5, 0*Z(11) ], [ Z(11), Z(11), Z(11)^9, Z(11)^2 ]], [[ Z(11)^3, Z(11), Z(11)^6, Z(11)^4 ], [ Z(11)^5, Z(11)^4, Z(11)^5, Z(11)^3 ], [ Z(11)^3, Z(11)^4, Z(11)^2, 0*Z(11) ], [ Z(11)^8, Z(11)^4, Z(11)^7, Z(11)^4 ]], [[ Z(11)^8, Z(11), Z(11)^6, Z(11)^3 ], [ Z(11)^5, Z(11)^9, Z(11)^2, Z(11)^6 ], [ Z(11)^9, Z(11)^2, Z(11)^0, Z(11)^6 ], [ 0*Z(11), Z(11)^9, Z(11)^0, Z(11)^2 ]], [[ Z(11)^6, 0*Z(11), 0*Z(11), 0*Z(11) ], [ Z(11)^7, Z(11)^4, Z(11)^5, 0*Z(11) ], [ Z(11)^9, Z(11)^9, Z(11)^4, 0*Z(11) ], [ Z(11)^8, Z(11)^9, Z(11)^2, Z(11)^0 ]], [[ Z(11), Z(11)^6, Z(11)^0, Z(11)^6 ], [ Z(11)^3, Z(11)^3, Z(11)^6, Z(11)^4 ], [ Z(11)^5, Z(11)^4, Z(11), 0*Z(11) ], [ Z(11)^8, Z(11)^9, 0*Z(11), Z(11)^5 ]], [[ Z(11)^8, 0*Z(11), 0*Z(11), 0*Z(11) ], [ 0*Z(11), Z(11)^8, 0*Z(11), 0*Z(11) ], [ 0*Z(11), 0*Z(11), Z(11)^8, 0*Z(11) ], [ 0*Z(11), 0*Z(11), 0*Z(11), Z(11)^8 ]], [[ Z(11)^3, 0*Z(11), 0*Z(11), 0*Z(11) ], [ 0*Z(11), Z(11)^3, 0*Z(11), 0*Z(11) ], [ 0*Z(11), 0*Z(11), Z(11)^3, 0*Z(11) ], [ 0*Z(11), 0*Z(11), 0*Z(11), Z(11)^3 ]], [[ 0*Z(11), Z(11)^5, Z(11)^8, Z(11)^4 ], [ Z(11)^5, Z(11)^3, Z(11)^8, Z(11)^8 ], [ Z(11)^9, Z(11)^7, Z(11)^2, Z(11)^0 ], [ 0*Z(11), Z(11)^9, Z(11)^0, Z(11)^0 ]]]);

 
# Booleans 
booleans_532400_d := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true);