//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;

//irreducible, fixed by auto
_LR`G := sub<GL(64,Integers()) |
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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,
  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
1,1,0,-1,0,0,-1,0,1,0,1,-1,-1,0,0,0,0,0,0,0,0,0,1,1,0,1,-1,0,0,0,
  0,0,0,0,-1,0,1,0,0,1,-1,0,0,0,0,0,0,0,-1,0,-1,1,0,1,-1,1,1,1,0,-1,
  1,0,-1,1,
0,0,0,0,0,1,0,0,1,0,0,0,0,0,-1,-1,0,0,0,1,0,-1,1,0,-1,0,0,0,0,0,0,
  0,0,1,0,0,1,1,1,0,0,-1,-1,0,0,-1,0,1,0,1,0,1,0,0,-1,0,0,0,0,0,0,
  0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,
  1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-1,0,1,1,0,-1,0,-1,-1,1,0,1,0,-1,0,1,0,0,0,-1,0,0,-1,0,0,0,1,1,0,
  1,1,-1,-1,-1,0,1,-1,-1,0,-1,0,1,1,1,-1,1,0,-1,0,-1,0,-1,1,0,1,-1,
  0,-1,1,0,-1,1,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]>;
return _LR;
