# Group 399300.k 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(4151264827863448657103696395341353646510930094550017910282557150913880435418962780139809043196076843797365165050970339486684150125900319939,399300); a := GPC.1; b := GPC.4; c := GPC.6; d := GPC.7;
GPerm := Group( (1,2,7,13,28,22,4,16,12,15,24,23,14,30,31)(3,8,25,19,10,26,6,9,21,5,17,20,18,11,29)(27,33,32)(34,35,38,37,36), (34,36,37,38,35), (1,3,6,19,15,18,32,14,5,13,4)(2,8,9,10,24,11,27,30,17,28,16)(7,20,29,21,12,31,23,25,22,33,26)(34,37,35,36,38), (34,36,37,38,35)(39,40)(41,42), (1,4,13,5,14,32,18,15,19,6,3)(2,9,24,27,17,16,8,10,11,30,28)(7,21,23,33,20,12,25,26,29,31,22)(34,35,38,37,36), (1,5,18,6,4,14,15,3,13,32,19)(2,10,27,28,8,24,30,16,9,11,17)(7,22,31,29,26,25,12,20,33,23,21)(34,38,36,35,37)(39,40)(41,42), (1,6,3,14,15)(2,11,17,8,16)(4,5,13,19,32)(7,23,21,26,20)(9,24,10,28,27)(22,29,31,33,25), (2,12,10,26,30,25,11,21,27,31)(3,15,18,13,19)(4,14,32,6,5)(7,24,20,8,23,17,33,16,29,28)(9,22)(34,37,35,36,38)(39,41,40,42) );
GLFp := Group([[[ 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)^5, Z(11)^4, Z(11)^7, Z(11)^6 ], [ Z(11)^8, Z(11)^0, Z(11), Z(11)^6 ], [ Z(11)^2, Z(11)^4, Z(11)^0, 0*Z(11) ], [ Z(11)^9, Z(11)^8, Z(11)^3, Z(11)^5 ]], [[ Z(11)^3, Z(11)^8, Z(11)^2, Z(11)^3 ], [ Z(11), Z(11)^2, Z(11), Z(11)^9 ], [ Z(11)^8, Z(11)^7, Z(11)^0, Z(11) ], [ Z(11)^2, Z(11)^2, Z(11)^3, 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) ], [ 0*Z(11), 0*Z(11), 0*Z(11), Z(11)^3 ]], [[ 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 ]], [[ 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 ]], [[ 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 ]]]);

 
# Booleans 
booleans_399300_k := 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);