//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 3.M22 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, a*b^-1*a ] ]
                  where a is (_LR`F).1 where b is (_LR`F).2;
//four constituents

_LR`G :=
/*
Original group: c9Group("3m22p")
Direct integral method
Schur index: 1
Character: ( 180, -12, -90, -90, 0, 4, 4, 0, 6, 6, 0, 0, 0, -2, -2, -4, 4, 4, 
-2, -2, -2, -2, 0, 0, 1, 1, 1, 1, 2, 2, -2, -2, -2, -2 )
*/

MatrixGroup<180,IntegerRing() |
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176,-131,82,145,-31,-42,236,105,23,-50,65])>;

return _LR;
