# Group 399300.d downloaded from the LMFDB on 17 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(20829329527180525648988365884303582157094255404798696767285747195880466305202287640987510607790249063658131968519936394103199039,399300); a := GPC.1; b := GPC.3; c := GPC.5; d := GPC.6;
GPerm := Group( (34,35,36,38,37), (1,2,5,16,15,6,19,13,4,12,17)(3,7,18,33,10,11,22,32,14,29,30)(8,23,27,25,9,26,21,31,20,24,28)(34,36,37,35,38), (34,35,36,38,37)(39,40), (2,6,16,15,12)(3,8,7,20,10,28,18,26,32,23)(4,13,5,17,19)(9,14,24,33,27,30,25,29,21,22)(11,31)(39,40), (1,3,9)(2,7,21,12,29,8,15,10,23,16,33,28,6,11,25)(4,14,24,19,22,26,17,30,27,5,18,20,13,32,31)(34,35,36,38,37)(39,40), (1,2,5,16,15,6,19,13,4,12,17)(3,10,14,7,11,29,18,22,30,33,32)(8,20,26,27,28,31,9,23,24,21,25)(34,37,38,36,35), (3,11,30,10,29,33,14,18,32,7,22)(8,24,31,26,25,23,28,20,21,9,27)(34,38,35,37,36)(39,40), (1,4,15,19,6)(2,5,13,17,16)(3,7,22,29,18)(8,25,31,26,21)(9,23,20,28,24)(10,30,32,33,11)(34,38,35,37,36) );
GLFp := Group([[[ Z(11)^5, Z(11), Z(11)^3, Z(11)^8 ], [ Z(11)^6, Z(11)^4, Z(11)^9, 0*Z(11) ], [ Z(11)^6, Z(11)^4, Z(11)^7, Z(11) ], [ Z(11)^0, Z(11)^6, Z(11)^0, Z(11)^8 ]], [[ 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), Z(11)^3, Z(11)^4, 0*Z(11) ], [ Z(11)^0, Z(11)^4, Z(11)^3, Z(11)^3 ], [ Z(11)^8, Z(11), Z(11)^4, Z(11)^7 ], [ Z(11)^9, Z(11)^8, Z(11)^3, Z(11)^5 ]], [[ 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)^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_399300_d := rec( 
Agroup := true,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := false);