//Standard generators of L2(23) are a, b where a has order 2,
//b has order 3 and ab has order 23.
//Standard generators of 2.L2(23) = SL2(23) are preimages A, B where
//B has order 3 and AB has order 23. 
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [a^-1, b^-1] ]
             where a is (_LR`F).1 where b is (_LR`F).2;
//irreducible, fixed by auto
_LR`G := sub<GL(22,Integers()) |
\[ -1,-1,0,1,0,-1,0,-1,0,0,0,0,0,-1,-1,0,-1,1,0,-1,1,
-1,1,1,0,-1,0,1,0,1,0,1,0,0,0,1,0,0,1,-1,0,0,-1,0,0,
-1,0,0,-1,0,1,-1,0,0,0,0,0,0,0,0,-1,0,0,0,1,-1,0,0,0,
0,1,0,0,0,0,0,0,0,-1,-1,-1,1,0,1,0,0,0,1,-1,-1,0,0,0,
0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,0,1,
0,1,0,0,0,0,-1,0,1,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,1,-1,
-1,1,0,0,0,0,1,0,1,0,0,0,1,0,-1,0,-1,-1,0,0,-1,0,0,
-1,1,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,-1,-1,0,0,-1,0,1,-1,1,0,0,0,0,0,
0,0,0,0,1,1,0,0,-1,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,
0,0,0,0,-1,0,1,0,0,0,1,0,-1,0,1,-1,0,1,-1,0,-1,-1,-1,
0,0,0,0,-1,0,0,0,0,-1,0,0,0,0,1,0,0,0,0,1,0,1,-1,-1,
0,0,0,0,0,0,0,0,0,1,0,-1,1,0,0,0,0,0,0,0,0,1,1,0,0,
1,1,0,0,1,0,0,-1,0,1,1,1,-1,0,0,-1,1,0,-1,0,1,-1,0,0,
-1,0,0,0,0,0,0,0,1,-1,1,-1,0,1,0,0,-1,0,0,-1,1,0,0,0,
0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,0,0,
-1,0,0,1,0,0,0,0,-1,1,0,0,1,0,0,1,1,0,0,0,0,0,-1,0,
0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,-1,1,0,0,0,0,-1,0,0,-1,-1,0,0,-1,0,-1,1,1,-1,-1,0,0,
0,0,0,-1 ],
\[ 0,1,0,0,1,-1,-1,1,1,-1,-1,0,1,1,0,-1,0,0,0,0,0,0,1,
0,0,-1,-1,1,1,0,0,0,0,0,-1,0,1,0,0,-1,0,1,0,0,0,0,0,
0,0,0,0,0,1,-1,-1,0,0,1,0,0,0,0,0,0,0,0,-1,0,0,0,1,
0,0,0,0,1,0,1,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
0,0,1,0,1,0,0,-1,0,1,0,0,0,0,0,0,0,-1,0,1,0,1,0,0,0,
1,0,0,1,-1,0,0,0,1,0,0,0,0,0,-1,1,0,1,0,0,1,0,0,-1,
-1,-1,0,0,0,0,0,0,0,-1,-1,0,1,0,0,0,-1,-1,1,1,0,0,-1,
0,1,0,0,0,-1,0,0,1,1,0,-1,0,1,0,1,0,0,0,0,0,1,0,0,1,
-1,1,0,-1,0,0,1,0,1,1,-1,-1,0,-1,0,0,0,0,0,-1,0,0,0,
1,-1,0,0,1,0,0,0,-1,1,0,1,0,0,1,-1,1,1,0,0,1,0,0,0,
-1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,-1,1,0,0,1,
1,0,-1,0,0,0,1,0,0,0,0,0,1,0,-1,0,0,0,1,0,0,0,-1,-1,
0,0,0,0,0,0,0,1,0,0,-1,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,-2,-1,0,-2,0,0,-1,
0,0,1,0,1,0,1,0,0,0,-1,0,1,-1,-1,0,1,0,1,0,1,0,1,0,
-1,1,-1,-1,0,1,0,0,0,0,0,1,0,-1,0,-1,0,0,1,0,1,-1,-1,
1,-1,-1,0,0,-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,0,0,-1,-1,0,1,0,-1,0,-1,0,0,0,1,0,-1,0,
0,-1,1,0,0,1,0,0,0,0,0,0,1,0,1,-1,0,1,0,0,0,0,0,1,0,
1,0,-1,1,1,2,0,0,1,0,-1,1,-1,0,0,-1,0,1,-1,0,1,0,1,0,
-1,1 ] >;

return _LR;
