//Standard generators of the Janko group J2 are a and b where a is in class 2B,
//b is in class 3B, ab has order 7 and ababb has order 12.
_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(36,Integers()) |
\[ 0,-1,0,0,0,0,-1,1,0,0,1,0,0,0,0,0,-1,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,-1,1,-1,0,1,
0,1,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,1,0,0,0,0,1,0,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,1,-1,1,-1,0,1,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,1,-1,0,0,-1,0,0,0,1,0,1,-1,0,0,0,-1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,-1,0,0,-1,0,-1,-1,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,-1,0,0,
0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,-1,0,1,0,0,0,0,1,0,0,0,0,0,-1,-1,-1,0,0,
-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,
0,0,0,0,0,0,1,1,0,1,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,
0,0,0,0,-1,0,0,0,0,-1,0,0,-1,0,0,0,0,-1,-1,-1,0,0,0,
0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,
1,0,0,0,0,0,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,-1,0,0,0,0,-1,0,0,0,0,0,1,1,1,0,0,1,0,0,
-1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,-1,0,0,0,0,0,0,0,
0,0,1,0,1,1,1,1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-1,1,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,-1,0,0,1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,
0,0,0,0,1,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,1,0,0,1,0,0,1,0,0,0,0,0,-1,0,-1,-1,-1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,-1,0,0,0,0,0,0,1,0,
0,0,0,1,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,
0,0,1,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,
0,-1,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,
0,-1,0,0,0,0,0,0,1,0,1,1,1,1,1,-1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,-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,-1,
0,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,-1,0,1,0,0,-1,0,-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,-1,-1,0,0,0,0,0,
-1,0,0,0,0,-1,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,1,
0,0,1,-1,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,-1,0,0,0,1,0,0,0,0,1,0,1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,1,0,0,0,0,0,0,-1,0,-1,-1,-1,-1,-1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,-1,0,0,-1,0,0,0,0,0,0,
1,0,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
0,-1,0,0,-1,0,0,0,0,0,-1,1,0,1,1,1,0,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0,0,0,
-1,0,0,-1,-1,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,-1,0,0,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,-1,0,0,0,1,0,
1,0,0,0,0,0,0,0,-1,2,0,0,1,1,0,-1,-1,0,0,0,0,0,1,1,
1,-1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,-1,0,0,0,0,0,-1,0,0,1,-1,0,0,0,0,0,1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,0,
1,0,-1,-1,1,0,0,0,0,0,0,0,1,0,0,0,0,0 ],
\[ 0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,-1,0,0,-1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,1,-1,-1,0,-1,-1,
0,-1,0,0,-1,0,-1,1,0,0,0,0,0,0,1,0,0,0,-1,0,0,0,1,0,
-1,0,-1,0,0,1,0,-1,1,0,0,1,0,0,1,-1,1,0,1,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,-1,0,-1,-1,0,-1,
-1,1,-1,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
0,0,0,0,0,0,1,0,0,1,0,0,1,-1,0,0,0,1,0,1,0,0,0,0,0,
0,0,0,0,-1,0,0,0,0,0,-1,0,0,0,-1,-1,0,1,0,0,0,0,0,1,
0,0,1,-1,0,0,1,-1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,-1,0,
1,0,-1,0,0,0,0,-1,1,-1,0,1,0,1,0,0,1,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,
0,0,1,1,0,0,1,0,0,0,1,-1,0,0,0,-1,0,0,0,1,0,0,0,-1,
0,1,0,0,1,0,1,0,1,1,0,-1,0,1,0,1,0,0,0,0,0,0,0,0,0,
0,0,-1,0,0,0,1,0,-1,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,
-1,0,-1,0,0,-1,0,0,0,0,0,0,0,0,1,0,0,0,-1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,-1,0,0,0,
0,0,0,-1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,-1,0,-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,
0,1,0,0,0,1,0,0,0,0,1,-1,0,0,1,0,0,0,0,0,1,0,0,0,0,
0,0,0,0,0,-1,-1,0,0,0,1,0,0,0,-1,0,0,0,0,1,0,1,0,1,
0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,
0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,
0,1,0,-1,0,0,0,0,0,0,-1,0,0,0,0,0,-1,0,0,-1,0,-1,-1,
-1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,1,1,0,1,0,0,0,0,
-1,1,0,1,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,-1,0,0,0,
0,0,0,0,-1,-1,0,0,-1,0,0,0,0,-1,0,0,-1,0,0,0,0,-1,-1,
0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,-1,0,0,-1,0,-1,0,0,0,
0,0,-1,0,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,
0,1,0,0,0,0,0,1,0,0,-1,0,-1,0,0,0,0,0,0,0,0,1,1,1,1,
0,0,0,0,0,-1,0,0,0,-1,0,0,0,0,1,0,-1,0,1,0,1,-1,-1,
-1,0,0,0,0,0,1,0,0,0,0,0,1,-1,1,0,0,0,0,0,-1,0,1,0,
0,1,0,0,0,-1,0,-1,0,0,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0,
0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,-1,0,0,1,0,0,0,0,-1,1,
0,0,1,0,0,1,0,1,1,0,0,0,0,0,0,0,-1,0,0,0,-1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,-1,1,1,0,1,0,1,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,-1,0,0,0,1,-1,1,
1,0,1,1,1,2,1,1,1,0,-1,0,1,-1,0,0,0,-1,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,1,0,1,0,-1,-1,0,-1,0,-1,0,-1,0,-1,0,
0,0,0,0,0,0,0,0,0,-1,0,0,0,0,-1,0,0,-1,0,1,0,1,0,0,
0,0,-1,0,0,0,0,0,0,-1,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,
-1,0,0,0,-1,0,1,0,0,0,0,1,0,0,0,0,0,-1,-1,-1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,1,0,0,
1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,-1,
0,-1,1,0,0,0,0,0,0,0,0,-1,-1,-1,0,0,0,0,-1,0,0,0,0,0,
0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,-1,1,0,0,0,0,0,
0,0,0,0,0,0,-1,0,0,0,0,0,0,-1,0,0,0,1,0,1,0,-1,0,0,
0,-1,0,1,0,0,0,0,1,0,0,0,0,0,-1,-1,0,0,0,-1,0,0,0,0,
0,0,0,0,1,0,0,-1,0,0,-1,0,0,0,0,-1,0,0,-1,0,-1,0,1,1,
0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,1,0,0,0,-1,1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,-1,0,
0,-1,0,-1,0,0,0,0,0,0,1,0,1,-1,0,-1,0,1,0,0,1,0,0,0,
0,1,0,2,-1,1,0,1,0,0,0,-1,0,0,0,0,0,0,0,-1,-1,0,-1,
-1,-1,1,1,1,-1,0,0,0,1,0,0,1,-1,0,0,0,1,-1,0,0,0,0,1,
1,0,0,0,0,0,0,0,0,0,0 ] >;

return _LR;
