//Standard generators of L3(4) are a and b where a has order 2, b has
//order 4, ab has order 7 and abb has order 5.
//Standard generators of 3.L3(4) are preimages A, B where A has order 2
//and B has order 4.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [ a, b^2*a*b^2*a*b*a*b*a*b^-1*a*b^2*a*b^2 ],
       //L34.2_1 = field x duality - order 2 - not same as in Online ATLAS.
            [ a, b^-1*a*b^2*a*b^-1*a*b^2*a*b*a*b^2*a*b^-1],
       //L34.3 = diagonal - order 3
            [ a, (b^-1*a*b^2*a*b^-1*a*b^2*a*b*a*b^2*a*b^-1)^-1]]
            //diagonal x duality - order 2
            //[ a, b^-1 ] ] //L34.2_3 = duality  - order 2
                  where a is (_LR`F).1 where b is (_LR`F).2;

//two constituents, fixed by AI[1], interchanged by AI[3], mapped to
//inequiv reps by AI[2] (so 6 reps altogether)
_LR`G := sub<GL(30,Integers()) |
\[ 0,0,-1,0,0,0,0,-1,-1,0,0,0,1,-1,1,0,0,1,0,0,-1,0,1,
-1,0,0,0,0,0,0,1,0,0,0,1,0,0,-1,-1,0,0,1,1,0,0,0,1,
1,0,-1,-1,0,0,0,0,0,0,0,1,0,0,0,-1,0,0,0,0,-1,-1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,
0,0,0,0,0,-1,0,-1,1,0,-1,0,0,0,0,0,1,0,0,0,0,0,-1,0,
-1,0,0,0,0,0,0,1,0,0,0,-1,0,0,-1,0,0,-1,0,0,1,1,0,-1,
0,0,1,1,-1,0,0,1,1,0,0,0,0,1,2,0,1,0,0,1,-1,0,1,-1,
0,-1,1,0,0,1,0,-1,0,1,0,0,1,0,1,0,0,0,0,1,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,-1,0,0,0,1,1,0,0,0,0,0,0,0,0,
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,
0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,
0,0,0,-1,0,0,0,0,0,-1,0,-1,0,0,-1,0,0,1,0,0,-1,1,0,0,
0,0,0,0,0,1,0,0,-1,0,0,-1,0,0,0,-1,-1,0,-1,0,0,0,0,1,
0,0,0,0,0,0,0,0,0,0,1,1,0,-1,0,0,0,0,0,-1,1,-1,0,0,
0,0,0,1,0,0,0,-1,1,0,0,-1,-1,0,1,1,-1,-1,0,0,0,-1,-1,
0,0,0,1,0,0,0,-1,0,0,1,-1,1,0,1,1,-1,0,1,0,0,-1,0,1,
1,1,-1,0,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0,0,0,-1,0,0,
0,0,-1,0,0,0,1,0,0,0,0,0,0,1,-1,0,0,0,1,0,-1,-1,0,-1,
0,1,-1,1,0,0,1,0,0,-1,0,0,-1,1,0,0,0,0,0,0,1,0,0,1,
1,0,0,0,1,-1,0,0,1,-1,-1,0,0,0,0,0,-1,-2,0,1,0,-1,0,
1,0,0,0,0,0,0,-1,0,0,0,-1,1,-1,1,0,0,0,1,0,1,0,0,1,
1,0,0,0,1,1,0,0,0,1,-1,0,0,-1,0,1,1,0,1,-1,1,0,0,-1,
1,1,0,0,0,1,1,0,0,0,0,1,0,0,0,-1,-1,-1,0,0,0,-1,-1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,-1,1,0,0,0,
0,0,0,0,0,0,-1,0,0,0,0,-1,-1,1,1,1,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,-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,
0,0,1,1,0,0,-1,0,0,1,0,0,-1,0,1,0,0,0,0,1,1,0,0,0,
-1,1,-1,0,0,-1,0,0,1,0,-1,0,0,0,0,0,0,0,0,-1,0,-1,0,
0,0,-1,-1,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,-1,0,0,0,0,
0,0,1,-1,0,0,0,0,0,0,1,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,
0,-1,-1,0,0,0,0,1,1,0,1,-1,0,1,1,-1,1,1,0,1,-1,0,1,0,
0,-1,0,0,0,1,-1,0,0,0,1,0,1,-2,0,0,-1,0,0,0,-1,0,0,
-1,0,-2,1,0,0,1,0,0,-1,1,2,-1,0,0,1,0,-1,0,1,-1,2,0,
-1,1,0,0,0,0,-1,1,-1,-1,1,1,-1,0,0,0,0,-1,0,1,0,0,0,
-1,0,0,-1,0,0,0,1,-1,1,0,0,0,1,0,0,1,-1,0,1,0,0,0,0,
1,-1,0,0,0,0,0,0,0 ],
\[ 0,0,0,0,0,1,0,0,0,1,0,0,-1,0,0,0,0,-1,0,0,1,-1,-1,
0,1,-1,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,-1,1,-1,0,0,
-1,0,0,1,0,-1,1,0,0,0,0,0,0,-1,2,-1,0,0,-1,0,1,1,1,1,
0,0,1,0,0,0,0,0,0,1,0,0,1,0,-1,-1,0,0,0,0,1,-2,0,-1,
0,0,0,1,0,1,0,0,0,1,0,0,0,-1,0,1,0,1,0,0,-1,-1,0,-1,
0,1,0,0,0,0,1,-1,-1,0,0,-1,1,0,0,0,0,0,0,0,0,-1,-1,0,
0,0,0,0,0,1,0,1,-1,0,0,0,-1,0,0,0,-1,0,0,0,0,0,-1,1,
1,0,0,-1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,-1,
0,-1,0,0,0,-1,0,0,1,0,0,-1,0,0,1,1,-1,0,0,-1,0,0,0,0,
0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,
-1,0,0,0,0,0,0,0,-1,0,-1,-1,0,-1,0,0,-1,0,1,1,0,0,0,
-1,0,1,1,0,0,0,-1,1,-1,0,0,-1,0,0,0,0,0,0,0,0,1,0,0,
0,1,1,1,0,0,0,0,0,0,0,0,0,-1,1,-1,0,0,0,0,0,0,1,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,0,0,0,-1,1,-1,0,0,0,
-1,0,0,1,0,-1,0,0,0,0,-1,0,1,1,0,-1,0,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,-1,-1,0,0,0,1,-1,1,0,0,1,1,0,-1,0,1,0,
0,0,0,0,0,0,0,0,-1,0,0,-1,0,1,1,0,1,-1,-1,1,0,-1,1,0,
0,1,1,0,-1,0,1,0,0,0,0,0,0,0,-1,0,0,-1,1,0,1,-1,1,0,
0,1,0,-1,1,0,-1,0,0,1,0,0,0,0,-1,0,-1,0,0,-1,1,0,0,1,
0,-1,-1,0,-1,1,-1,0,0,1,-1,-1,0,0,0,-1,-1,0,0,0,0,-1,
0,0,0,-1,1,0,0,-1,0,-1,-1,-1,-1,2,0,0,1,1,0,1,0,0,-1,
0,0,1,-1,1,0,-1,0,0,0,0,-1,0,0,0,0,1,0,1,0,-1,-1,0,0,
-1,0,0,0,1,1,0,-1,-1,1,0,0,0,0,0,0,-2,0,0,0,0,0,0,-1,
0,-1,-1,-1,0,0,0,0,0,0,1,0,0,-1,-1,1,1,1,0,0,0,0,1,0,
0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,-1,0,1,0,-1,0,
0,1,0,0,1,-1,0,0,0,0,-1,0,0,0,1,1,0,1,0,0,1,0,0,0,0,
0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,1,1,-1,0,-1,0,1,-1,
-1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,-1,0,1,0,
0,1,0,1,0,1,0,0,0,0,0,-1,0,1,-1,0,0,0,1,0,1,-1,1,-1,
0,0,0,-1,0,-1,0,1,1,0,0,0,1,0,0,-1,-1,1,1,0,-1,0,0,1,
0,0,-1,1,1,0,0,0,-1,0,1,0,0,0,0,1,-1,1,-1,-1,1,0,0,
-1,0,1,-1,0,0,0,1,0,-1,1,0,0,0,0,0,-1,0,0,0,2,0,0,1,
1,0,0,0,0,0,-1,0,1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,1,1,
0,0,-2,0,0,-1,-1,0,-1,1,1,1,1,0,-1,0,1,1,1,0,1,0,1,
-1,0,0,1,0,0,1,1,1,0,-1,0,0,0,0,-1,-1,0,1,-1,0,0,0,
-2,-1,0,0,0,0,1,0,0,0,0,1,0,1,-1,1,0,1,0,0,0,0,0,-1,
-1,0,1,1,0,-1,0,-1,0,-1,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0 ] >;

return _LR;
