//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;

//one constituents
_LR`G :=
/*
Original group: c9Group("2u42p")
Direct induction from degree 1
Schur index: 1
Character: ( 120, -120, 0, 3, 3, 0, 6, 0, -4, 4, 0, -3, -3, 0, -3, 3, -3, 3, -6,
0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, 0, 0, 0 )
*/

MatrixGroup<120,IntegerRing() |
Matrix(SparseMatrix(120,120,\[
1,2,1,1,1,1,1,12,1,1,18,1,1,11,1,1,19,1,1,25,-1,
1,30,1,1,35,1,1,10,1,1,5,1,1,3,1,1,37,1,1,14,-1,
1,21,1,1,53,1,1,26,1,1,4,1,1,6,1,1,20,1,1,15,1,1,
69,1,1,23,1,1,67,1,1,7,-1,1,17,1,1,83,1,1,87,1,1,
90,-1,1,8,1,1,70,1,1,82,1,1,65,1,1,93,1,1,9,1,1,
36,-1,1,13,1,1,96,1,1,39,1,1,40,-1,1,41,1,1,94,1,1,
85,1,1,47,1,1,60,1,1,48,-1,1,44,1,1,46,-1,1,100,1,
1,50,-1,1,107,1,1,109,1,1,16,1,1,101,1,1,111,1,1,
99,1,1,57,1,1,58,-1,1,92,1,1,45,1,1,61,-1,1,62,1,
1,106,-1,1,112,1,1,33,1,1,72,1,1,24,1,1,86,1,1,
22,1,1,31,1,1,71,1,1,66,1,1,73,1,1,114,-1,1,98,1,
1,102,1,1,77,-1,1,118,1,1,79,1,1,80,-1,1,81,1,1,
32,1,1,27,1,1,119,1,1,43,1,1,68,1,1,28,1,1,88,-1,1,
116,1,1,29,-1,1,120,1,1,59,1,1,34,1,1,42,1,1,97,1,
1,38,1,1,95,1,1,75,1,1,56,1,1,49,1,1,54,1,1,76,1,
1,117,-1,1,115,-1,1,105,-1,1,63,-1,1,51,1,1,108,-1,
1,52,1,1,110,1,1,55,1,1,64,1,1,113,-1,1,74,-1,1,
104,-1,1,89,1,1,103,-1,1,78,1,1,84,1,1,91,1
])),Matrix(SparseMatrix(120,120,\[
1,3,1,1,6,1,1,13,1,1,16,1,1,17,-1,1,8,1,1,26,-1,1,
31,1,1,20,1,1,30,1,1,22,-1,1,40,-1,1,43,1,1,47,1,
1,51,1,1,35,1,1,46,1,1,55,1,1,41,1,1,62,1,1,10,1,
1,32,1,1,73,1,1,2,1,1,78,1,1,80,1,1,5,1,1,88,1,1,
53,1,1,45,1,1,24,1,1,54,1,1,12,1,1,1,1,1,87,1,1,
94,-1,1,23,1,1,77,1,1,82,1,1,58,1,1,66,1,1,21,1,1,
34,1,1,70,1,1,42,1,1,96,-1,1,104,-1,1,71,-1,1,52,-1,
1,76,1,1,18,1,1,106,1,1,105,-1,1,72,-1,1,56,1,1,15,1,
1,99,1,1,68,-1,1,19,1,1,36,1,1,93,-1,1,38,1,1,49,-1,
1,60,1,1,74,-1,1,100,1,1,97,1,1,33,1,1,81,1,1,39,1,
1,79,1,1,11,1,1,28,-1,1,84,1,1,117,1,1,112,1,1,9,1,
1,95,-1,1,85,-1,1,61,1,1,107,1,1,103,1,1,29,-1,1,
92,1,1,108,-1,1,4,1,1,86,1,1,37,-1,1,118,1,1,63,1,
1,102,1,1,114,1,1,7,1,1,98,1,1,89,-1,1,27,1,1,109,1,
1,64,-1,1,91,1,1,59,1,1,57,1,1,101,1,1,44,1,1,75,1,
1,113,-1,1,90,1,1,119,1,1,48,-1,1,111,1,1,67,1,1,
110,1,1,115,1,1,83,-1,1,65,-1,1,120,-1,1,69,1,1,
14,-1,1,25,1,1,116,1,1,50,-1
]))>;

return _LR;
