//Standard generators of the Mathieu group M22 are a and b where a has order 2,
//b is in class 4A, ab has order 11 and ababb has order 11.
//Standard generators of the double cover 2.M22 are preimages A and B where A is
//in +2A, B is in -4A and AB has order 11 (any two of these conditions imply the
//third). An equivalent set of conditions is that AB has order 11 and ABABB has
//order 11.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [ a, a*b^-1*a ] ]
                  where a is (_LR`F).1 where b is (_LR`F).2;
//two constituents, fixed by _LR`AI[1].

_LR`G :=
MatrixGroup<10, ext<K|Polynomial(K, [2, 1, 1])> where K is RationalField() |
[[2,0],[2,0],[
0,-1],[1,0],[1,1],[
0,-1],[0,1],[
0,0],[0,-1],[0,1],[
-1,0],[-6,-1],[
2,0],[-2,2],[-2,-3],[
0,0],[-1,-2],[
0,-2],[2,2],[2,-1],[
-1,-1],[-2,-2],[
0,0],[-1,0],[0,-1],[
-1,0],[2,0],[
0,0],[-1,0],[2,0],[
-2,-1],[-6,2],[
-2,-2],[3,3],[-4,-2],[
-2,0],[0,-1],[
-4,-2],[2,1],[2,-3],[
1,-1],[-2,-5],[
2,0],[-3,0],[2,-1],[
0,-1],[2,1],[
2,-1],[-2,0],[4,3],[
0,0],[0,0],[
-1,0],[0,-1],[1,0],[
0,0],[0,0],[0,
0],[-1,0],[0,0],[
0,0],[1,-2],[
0,1],[-1,-2],[3,1],[
0,0],[2,0],[2,
1],[-2,0],[0,1],[
-1,0],[2,3],[
-2,0],[2,0],[-1,1],[
0,1],[0,0],[
-1,1],[1,0],[-2,-2],[
0,1],[4,5],[
-2,0],[4,0],[-2,2],[
0,1],[-2,0],[
-2,1],[1,-1],[-4,-2],[
0,1],[0,2],[1,
1],[-1,0],[-1,-1],[
1,1],[-2,-1],[
0,0],[2,1],[-1,-1]],
[[-1,-1],[-1,-2],[
0,0],[-1,-1],[
1,0],[0,0],[1,0],[
0,0],[-1,0],[
1,1],[0,0],[-1,0],[
0,0],[1,1],[
-1,0],[0,0],[1,0],[
0,0],[0,0],[0,
-1],[0,0],[-3,2],[
0,-2],[3,4],[
-4,-1],[-1,-1],[-1,0],[
-3,-2],[3,0],[
1,-2],[0,1],[5,3],[
-2,1],[1,-2],[
1,2],[1,1],[-1,0],[
1,2],[-1,-1],[
-4,-1],[0,0],[-3,1],[
0,-2],[2,3],[
-3,-1],[-1,-1],[-1,0],[
-2,-2],[2,0],[
1,-1],[0,-1],[2,-1],[
-2,0],[0,-2],[
2,1],[-1,0],[2,1],[
0,1],[-2,-1],[
0,1],[1,0],[4,0],[
-1,0],[0,-1],[
1,1],[0,0],[1,2],[
0,1],[-1,-1],[
0,1],[0,1],[4,0],[
0,2],[-3,-3],[
3,1],[2,1],[-1,0],[
3,2],[-2,0],[
-2,1],[2,1],[5,-2],[
2,2],[-4,-3],[
4,1],[2,0],[0,1],[
4,1],[-2,0],[
-1,3],[1,0],[0,-4],[
3,2],[-5,-1],[
2,-1],[2,0],[1,0],[
4,0],[-1,1],[
1,2]]>;

return _LR;
