_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [a, b^(a*b*a*b*b*a*b)] ] where a is (_LR`F).1 where b is (_LR`F).2;
//Standard generators of the Suzuki group Suz are a and b where a is in class
//2B, b is in class 3B, ab has order 13 and ababb has order 15.
//Standard generators of 6.Suz are preimages A and B where A has order 4, B has
//order 3 and AB has order 13.
//two constituents, interchanged by _LR`AI[1]
_LR`G := sub<GL(24,Integers()) |
\[ 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,
0,0,0,0,0,0,0,0,0,0,-1,0,2,2,0,0,1,3,-2,0,-2,-1,-2,
-3,0,1,0,0,0,0,0,-1,-2,-2,0,-1,-2,0,0,0,-3,-2,0,-2,1,
-1,3,1,-1,-1,0,0,0,0,1,1,2,0,-1,-1,0,2,0,0,-2,1,-2,-2,
-1,-2,1,-2,-1,0,0,0,0,0,1,0,1,-1,1,0,-2,-2,0,0,-1,-3,
2,0,2,1,2,3,0,-1,0,0,0,0,0,1,1,2,0,2,1,1,-2,1,0,0,1,
-2,-1,0,2,2,1,2,-1,1,-2,-2,0,0,0,0,-2,-2,-1,0,-1,-3,0,
0,2,3,0,-1,-2,0,-2,-1,-1,-2,2,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,-1,-1,0,0,0,0 ],
\[ -1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-1,-1,2,-1,0,0,
-1,2,1,0,-2,-2,-1,-2,1,-1,2,2,0,0,0,0,2,2,1,0,1,3,0,
0,-2,-3,0,1,2,0,2,1,1,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,0,0,0,0,-2,2,1,1,-4,-3,2,1,3,2,
-2,-1,-2,2,-2,1,-2,-2,2,-2,0,0,0,0,-2,-4,-1,0,3,-1,-1,
1,-2,1,1,-1,-2,-4,-1,-3,2,0,2,4,0,0,0,0,-2,-3,-1,-1,2,
-1,0,1,-1,2,0,-1,-2,-3,-1,-2,1,-1,3,3,0,0,0,0,3,1,1,0,
1,3,-1,-1,-2,-3,1,1,3,1,2,1,1,2,-3,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,-1,-1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,2,1,0,2,1,2,
-2,-1,-1,-4,2,1,4,1,1,1,0,1,-4,-1,0,0,1,0,-1,1,-2,-2,
-2,-1,1,-1,4,3,-1,1,-1,3,-1,0,-1,-1,1,-3,0,0,0,1 ] >;

return _LR;
