/*
Monster 3^{1+12}"2"Suz:2 as 78 x 78 matrices over GF(3).
Generators C,D,E.
Group is GG.
Field is FF.
Group elements A,B,C,D,E,F,G,H,I,J,K,aa,bb,gg,dd,ee,zz,hh.
*/

print "Loading group GG, field FF=GF(3), group elements A,B,C,D,E,F,G,H,I,J,K,aa,bb,gg,dd,ee,zz,hh.";

FF:=GF(3);

x:=CambridgeMatrix(1,FF,78,[
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y:=CambridgeMatrix(1,FF,78,[
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z:=CambridgeMatrix(1,FF,78,[
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GG<x,y,z>:=MatrixGroup<78,FF|x,y,z>;

C:=x;D:=y;E:=z;
A:=(C*D*D)^-2*(C*D)^14*(C*D*D)^2;
// If A and B are to be standard generators of 2"Suz then A needs inverting.
B:=D;
aa:=(C*D*(C*D*C*D^2)^2*(C*D)^2*(C*D*C*D^2)^2)^11;
bb:=(C*D)^-6*(C*D*(C*D*C*D^2)^2)^2*(C*D)^6;
gg:=(aa*bb^2*aa*bb*(aa*bb*aa*bb^2)^2)^10;
dd:=(aa*bb*aa*bb^2)^-4*aa*(aa*bb*aa*bb^2)^4;
ee:=(aa*bb)^-1*((aa*bb)^3*bb)^3*aa*bb;
F:=bb^5;
G:=((dd*ee)^3*ee)^11;
H:=dd*G;
I:=ee*G;
zz:=(H*I)^3*I*H*I;
// OJ:=(zz*(zz^2*gg)^3*zz)^-1*(zz^2*gg)^2; // This is wrong.
J:=((zz^2*gg)^4*zz)^-1*zz*(zz^2*gg)^4;
hh:=(D^-1*E*D*G)^2;
K:=(zz*(hh*zz^2)^4)^-1*(hh*zz^2)^4*zz;

o8a:=(H*J*I*K)^6*I*K*(H*J*I*K)^2*I*K*(H*J*I*K*I*K)^2;
o8b:=(H*K*I*J)^6*I*J*(H*K*I*J)^2*I*J*(H*K*I*J*I*J)^2;
// o8a and o8b should both have order 8.