//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.
//Standard generators of the double cover 2.J2 are preimages A and B where B has
//order 3, and AB has order 7.
_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;

//two constituents, interchanged by _LR`AI[1]
_LR`G :=
MatrixGroup<6, ext<K|Polynomial(K, [1, 1, 1, 1, 1])> where K is RationalField() 
|
[[7,0,5,6],[-2,-4,1,-7],[
-5,-1,-4,-2],[-5,-5,-2,-6],[
1,-1,2,0],[-2,2,-1,2],[
3,-1,1,0],[-2,-1,0,-3],[
0,1,-1,0],[-2,0,0,-2],[
0,0,1,0],[1,1,-2,0],[
3,0,1,1],[-2,-2,0,-2],[
-1,0,-1,-1],[-1,0,0,-2],[
0,0,1,0],[0,1,-1,0],[
9,-2,4,3],[-5,-5,1,-9],[
-3,2,-3,-2],[-5,-1,-1,-6],[
0,-1,1,-1],[0,2,-5,1],[
-2,5,-6,3],[10,3,5,9],[
1,-3,2,-3],[6,0,4,3],[
1,2,1,2],[-4,-3,-2,-7],[
6,-3,3,2],[-5,-4,0,-7],[
-3,1,-3,-2],[-3,-1,-1,-5],[
2,0,1,0],[0,0,-4,2]],
[[-2,0,1,-3],[-3,0,-3,-1],[
1,1,1,3],[0,1,0,2],[
-1,-1,-1,-1],[2,2,3,1],[
-1,-2,3,-4],[-6,0,-4,-3],[
1,2,0,4],[-3,0,-2,0],[
-1,-1,0,-1],[4,4,4,4],[
-10,-2,-6,-9],[1,6,-3,7],[
6,1,3,4],[4,4,1,6],[
-1,1,0,0],[3,-3,2,-2],[
-3,0,-3,0],[3,2,1,3],[
1,-2,0,0],[2,0,0,1],[
0,1,0,0],[-2,-2,-1,-2],[
-2,1,-3,-2],[3,2,1,4],[
1,0,1,0],[2,1,2,2],[
1,1,1,1],[1,-1,0,-3],[
-2,-2,-1,-1],[0,1,0,0],[
1,0,0,1],[0,0,-1,0],[
0,0,0,-1],[-1,-2,-1,0]]>;

return _LR;
