# Group 2662000.a 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(1441929371628022358098222723374343869687805798794806844069893513591011977259639750053736786067554403236939999930627285346169658884185602790483894442747765753211321091563508577931413064965554962176854161380114771532019295839250303039909,2662000); a := GPC.1; b := GPC.3; c := GPC.5; d := GPC.8; e := GPC.9;
GPerm := Group( (38,39,40,42,41), (1,2,6,9,4,14,5,3,8,12,11)(7,15,20,10,22,18,17,16,19,21,13)(23,24,29,31,26,30,25,28,32,33,27)(38,40,41,39,42), (34,35)(36,37)(38,39,40,42,41), (1,3,9,11,5,6,12,14,2,8,4)(7,18,13,22,21,10,19,20,16,15,17)(23,25,24,28,29,32,31,33,26,27,30)(38,41,42,40,39), (1,4,2,5,14,9,11,6,8,12)(7,10,21,13,15,18,20,16,17,22)(24,29,26,32,30,27,33,28,31,25)(34,35)(36,37)(38,41,42,40,39), (1,5,9,11,2)(3,8,6,14,12)(7,10,16,18,17)(13,21,22,15,19)(24,25,31,28,33,27,30,32,26,29)(36,37), (1,6,4,5,8,11,2,9,14,3,12)(7,19,18,20,13,16,22,15,21,17,10)(23,26,32,24,30,33,29,25,27,31,28)(34,35)(36,37)(38,42,39,41,40), (1,7,9,21,8,20,12,18,3,13)(2,10)(4,15,5,16,6,17,11,19,14,22)(23,27,29,26,33,30,25,31,24,28)(34,36)(35,37)(38,40,41,39,42), (1,6,2,3,4)(5,11,8,12,9)(7,20,15,16,22)(10,17,13,19,21)(23,27,30,29,33)(24,26,32,25,28), (1,2,11,9,5)(3,12,14,6,8)(7,17,15,16,20,19,10,21,22,13,18)(23,28,25,31,30)(24,27,26,32,33)(34,35)(36,37)(38,41,42,40,39) );
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)^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)^7, Z(11), Z(11)^7, Z(11)^7 ], [ Z(11)^8, Z(11)^6, Z(11)^8, Z(11)^3 ], [ Z(11)^0, Z(11), Z(11)^4, 0*Z(11) ], [ Z(11)^3, Z(11)^6, 0*Z(11), 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 ]], [[ Z(11)^9, Z(11)^2, Z(11)^8, Z(11) ], [ Z(11)^4, Z(11)^7, Z(11)^8, Z(11)^4 ], [ 0*Z(11), Z(11)^2, Z(11)^9, Z(11)^6 ], [ Z(11)^0, Z(11)^0, Z(11)^0, Z(11)^6 ]], [[ Z(11)^7, 0*Z(11), Z(11)^6, 0*Z(11) ], [ Z(11)^6, Z(11)^6, Z(11)^7, Z(11)^5 ], [ 0*Z(11), Z(11)^2, Z(11)^8, Z(11) ], [ 0*Z(11), Z(11)^6, Z(11)^2, Z(11)^8 ]], [[ 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_2662000_a := rec( 
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := false,
metacyclic := false,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := false);