//Standard generators of U4(2) = S4(3) are a, b where a is in class 2A,
//b has order 5 and ab has order 9.
//Standard generators of 2.U4(2) = Sp4(3) are preimages A,
//B where B has order 5 and AB has order 9.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [a, b^-1] ] where a is (_LR`F).1 where b is (_LR`F).2;

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

return _LR;
