# Group 798600.i 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(31604515881349254106337098671025999532963447253957555619836240604850642716357777911207517603740219760224589150850931104697896923625616727872397149815838462421604537731263758021030199039,798600); a := GPC.1; b := GPC.3; c := GPC.5; d := GPC.6; e := GPC.7;
GPerm := Group( (34,35,36,38,37), (1,2,6,19,5,18,17,4,7,9,16)(3,10,13,24,12,14,8,20,25,15,23)(11,27,21,31,26,30,22,32,28,29,33)(34,36,37,35,38), (2,7,9,17,5,16,19,6,18,4)(3,11,13,28,15,31,8,21,10,26)(12,30,14,29,24,27,20,22,23,32)(25,33)(34,36,37,35,38)(39,40), (34,35,36,38,37)(39,40), (1,3,11)(2,8,22,7,12,26,9,23,33,17,24,31,5,13,21,16,14,30,19,20,32,6,10,27,18,25,28,4,15,29)(34,35,36,38,37)(39,40), (1,2,6,19,5,18,17,4,7,9,16)(3,12,25,10,14,15,13,8,23,24,20)(11,28,30,21,33,32,26,27,29,22,31)(34,37,38,36,35), (1,4,16,18,17,7,2,9,19,6)(3,13,8,24,25,20,14,10,12,23)(21,26,28,30,33,29,32,31,22,27), (3,14,23,12,15,24,25,13,20,10,8)(11,29,32,30,31,27,33,28,22,26,21)(34,38,35,37,36)(39,40), (1,5,6,19,7)(2,9,18,4,17)(8,25,20,13,23)(10,14,24,12,15)(11,22,31,33,27)(21,30,29,32,28)(34,37,38,36,35) );
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), 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)^4, Z(11)^8, Z(11)^3, 0*Z(11) ], [ 0*Z(11), 0*Z(11), Z(11)^0, Z(11)^9 ], [ Z(11)^4, Z(11)^0, Z(11)^2, Z(11)^3 ], [ Z(11)^3, Z(11)^7, Z(11)^4, Z(11) ]], [[ Z(11), Z(11)^9, Z(11)^6, Z(11)^2 ], [ Z(11)^2, Z(11)^3, 0*Z(11), 0*Z(11) ], [ Z(11)^4, Z(11)^5, Z(11)^2, Z(11)^5 ], [ Z(11)^4, Z(11)^2, Z(11)^6, Z(11)^2 ]], [[ 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_798600_i := rec( 
Agroup := true,
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);