//standard generators for PSL(2,25), a order 2, b order 3, order(ab)=12.
//standard generators for SL(2,25), a order 4, b order 3, order(ab)=24,
//                                           order(abab^-1ab) = 13.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [a^-1, b^-1], //PSL(2,25).2_1 = PGL(2,25)
            [a, b^-1*a*b*a*b^-1*a*b*a*b^-1*a^-1],//PSL(2,25).2_1 = PSigmaL(2,25)
            [a^-1, a*b*a*b^-1*a*b*a*b^-1*a*b] ]
             where a is (_LR`F).1 where b is (_LR`F).2;
//irreducible fixed by all autos
_LR`G := sub<GL(26,Integers()) |
\[ 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,
0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,-1,0,0,1,-1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,1,
0,0,0,0,0,-1,-1,0,0,-1,0,0,1,0,0,0,0,1,0,0,1,0,0,1,
0,1,0,0,0,0,0,0,0,0,0,-1,-1,0,1,0,0,0,0,0,-1,0,0,0,
0,1,0,1,0,0,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,
0,0,0,0,0,-1,0,1,0,0,0,0,0,0,-1,1,0,0,0,-1,0,0,0,0,
0,1,1,-1,0,0,0,0,0,0,0,0,0,-1,0,0,-1,0,0,0,0,0,0,0,
0,0,0,1,1,0,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,-1,0,0,0,
0,0,1,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,-1,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,-1,0,0,-1,-1,0,
1,0,0,0,0,0,1,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,0,-1,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,-1,0,
1,-1,-1,-1,1,0,0,1,0,0,0,0,-1,0,0,-1,-1,0,0,0,0,0,1,
1,0,0,1,0,0,-1,0,0,0,0,0,1,0,0,0,0,-1,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
0,1,1,0,0,0,-1,0,-1,0,0,0,0,-1,0,0,-1,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,1,0,0,0,0,1,1,0,1,0,
0,0,0,0,1,1,0,0,1,-1,0,-1,0,0,0,0,0,1,0,0,0,1,0,-1,
0,1,0,0,0,0,-1,-1,0,0,-1,0,0,1,0,1,0,0,0,-1,0,0,0,0,
1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,1,0,0,0,0,0,
1,0,0,0,1,1,0,0,0,0,0,-1,0,0,-1,0,0,1,1,-1,0,0,1,-1,
0,1,0,0,1,0,0,-1,0,0,0,0,0,1,0,0,1,-1,0,0,0,0,0,0,0,
0,0,0,0,1,0,-1,0,0,0,0,1,0,0,0,0,0,-1,1,0,0,1,-1,0,
0,1,0,0,0,0,-1,0,1,0,0,0,-1,0,1 ],
\[ 0,0,0,0,0,0,0,0,0,0,-1,0,1,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,1,-1,0,0,-1,0,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,1,0,1,-1,0,0,0,0,0,-1,0,-1,0,0,0,0,1,0,0,
0,0,0,0,0,0,0,0,0,1,-1,0,0,0,1,0,-1,0,-1,0,0,0,0,0,
0,1,0,0,0,0,-1,0,0,0,1,0,0,1,0,0,1,-1,0,-1,-1,0,1,0,
0,0,0,0,0,0,0,0,0,0,-1,-1,-1,0,0,-1,0,0,1,0,0,1,0,0,
-1,0,1,0,0,1,0,1,0,0,0,0,0,0,-1,0,0,-1,0,0,0,1,0,0,
0,0,0,1,0,0,0,1,0,0,0,0,0,-1,0,0,0,0,0,0,-1,0,1,0,0,
0,-1,0,0,1,0,0,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,-1,0,0,0,-1,-1,0,0,-1,1,0,
1,0,0,0,0,0,-1,0,0,0,-1,0,1,0,-1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,0,0,
-1,1,0,0,0,0,0,1,0,-1,-1,1,0,-1,0,0,0,0,0,0,0,0,0,0,
-1,0,0,-1,-1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,-1,0,1,0,0,
0,0,0,0,0,0,0,-1,0,0,0,1,0,0,-1,0,0,0,0,0,0,1,0,0,0,
0,1,1,0,1,0,-1,0,-1,0,0,0,0,0,0,0,-1,0,1,0,0,0,1,0,
0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,1,1,1,1,0,0,0,-1,1,0,0,0,1,0,-1,0,1,-1,0,
0,1,0,0,0,-1,0,1,0,0,0,0,0,1,0,-1,0,-1,0,0,0,0,0,0,
0,0,0,-1,0,0,1,0,0,1,0,1,0,-1,0,0,0,0,0,0,0,0,0,-1,
0,1,0,0,0,0,0,0,1,0,0,0,0,-1,1,0,0,1,-1,0,-1,-1,0,1,
0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,-1,0,0,0,1,0,0,0,0,
-1,0,0,0,0,1,0,0,0,0,0,0,0,1,1,1,0,1,-1,0,0,0,0,0,
-1,0,1,1,-1,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,-1,0,0,1,1,
-1,0,0,0,-1,0,1,0,-1,1,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,
0,-1,1,-1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,-1,0 ] >;

return _LR;
