//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 integral method
Schur index: 2
Character: ( 80, -80, 0, 8, 8, 2, -4, 0, 0, 0, 0, -8, -8, -2, 0, 0, 0, 0, 4, 0, 
0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1 )
*/

MatrixGroup<160,IntegerRing() |
Matrix(SparseMatrix(160,160,\[
2,149,1,152,-1,3,149,-1,150,1,151,1,3,149,1,150,-1,
152,-1,1,149,1,1,5,1,2,7,1,8,-1,2,5,1,7,-1,3,5,1,
6,-1,7,-1,1,57,-1,1,58,-1,1,59,-1,1,60,-1,2,65,1,
68,-1,2,66,-1,68,-1,1,66,1,2,65,1,67,-1,1,17,-1,2,
19,-1,20,1,2,17,-1,19,1,3,17,-1,18,1,19,1,1,21,-1,
2,23,-1,24,1,2,21,-1,23,1,3,21,-1,22,1,23,1,1,25,-1,
2,27,-1,28,1,2,25,-1,27,1,3,25,-1,26,1,27,1,2,29,1,
31,-1,3,29,1,30,-1,32,-1,1,31,-1,2,31,-1,32,1,2,153,-1,
156,1,2,154,1,156,1,1,154,-1,2,153,-1,155,1,1,86,1,
1,85,-1,2,85,1,88,-1,2,86,1,87,1,3,97,1,98,-1,100,-1,
2,98,1,99,1,1,98,-1,3,97,1,98,-1,99,-1,2,45,-1,47,1,
3,45,-1,46,1,48,1,1,47,1,2,47,1,48,-1,1,49,1,2,51,1,
52,-1,2,49,1,51,-1,3,49,1,50,-1,51,-1,1,55,-1,3,53,1,
54,-1,55,-1,1,53,-1,3,53,-1,54,1,56,1,1,9,-1,1,10,-1,
1,11,-1,1,12,-1,1,114,1,4,113,1,114,-1,115,-1,116,-1,
3,113,-1,114,1,116,1,2,114,1,116,1,3,13,1,14,-1,15,-1,
1,15,1,4,13,1,14,-1,15,-1,16,-1,2,14,-1,15,-1,4,69,-1,
70,1,71,1,72,1,1,70,1,1,72,1,1,71,1,2,142,-1,144,-1,
2,141,-1,144,1,2,143,1,144,-1,1,144,-1,2,77,1,79,-1,3,
77,1,78,-1,80,-1,1,79,-1,2,79,-1,80,1,3,121,-1,122,1,
123,1,2,121,-1,124,1,1,124,-1,2,123,1,124,-1,1,38,-1,
1,37,1,2,37,-1,40,1,2,38,-1,39,-1,2,109,1,111,-1,3,
109,1,110,-1,112,-1,1,111,-1,2,111,-1,112,1,2,94,-1,
96,-1,2,93,-1,96,1,2,95,1,96,-1,1,96,-1,2,42,1,44,1,
1,43,-1,2,42,1,43,1,4,41,-1,42,1,43,1,44,1,1,129,1,
1,130,1,1,131,1,1,132,1,4,105,-1,106,1,107,1,108,1,
1,106,1,1,108,1,1,107,1,2,89,1,91,-1,3,89,1,90,-1,
92,-1,1,91,-1,2,91,-1,92,1,2,63,-1,64,1,1,61,1,2,
62,-1,63,-1,2,61,-1,64,1,2,118,-1,120,-1,2,117,-1,
120,1,2,119,1,120,-1,1,120,-1,2,82,-1,83,-1,3,81,1,
82,-1,84,-1,2,83,-1,84,1,1,83,-1,1,157,1,1,158,1,
1,159,1,1,160,1,1,101,1,1,102,1,1,103,1,1,104,1,2,
133,1,135,-1,3,133,1,134,-1,136,-1,1,135,-1,2,135,-1,
136,1,2,138,-1,140,-1,2,137,-1,140,1,2,139,1,140,-1,
1,140,-1,2,74,-1,76,-1,2,73,-1,76,1,2,75,1,76,-1,1,
76,-1,4,145,-1,146,1,147,1,148,1,1,146,1,1,148,1,1,
147,1,1,4,1,2,1,1,3,-1,4,1,-1,2,1,3,1,4,1,2,1,-1,
4,1,3,33,-1,34,1,35,1,1,35,-1,4,33,-1,34,1,35,1,36,1,
2,34,1,35,1,1,125,1,1,126,1,1,127,1,1,128,1
])),Matrix(SparseMatrix(160,160,\[
2,143,-1,144,1,4,141,1,142,-1,143,-1,144,-1,2,142,1,
144,1,3,141,-1,142,1,144,1,3,53,-1,54,1,55,1,2,53,-1,
56,1,1,56,-1,2,55,1,56,-1,1,84,1,2,82,1,83,1,3,81,1,
82,-1,83,-1,1,82,-1,1,1,-1,2,3,-1,4,1,2,1,-1,3,1,3,
1,-1,2,1,3,1,2,119,1,120,-1,1,117,-1,2,118,1,119,1,
2,117,1,120,-1,2,114,1,116,1,2,113,1,116,-1,2,115,-1,
116,1,1,116,1,2,126,-1,128,-1,1,127,1,2,126,-1,127,-1,
4,125,1,126,-1,127,-1,128,-1,2,122,-1,124,-1,1,123,1,
2,122,-1,123,-1,4,121,1,122,-1,123,-1,124,-1,3,17,1,
18,-1,20,-1,2,18,1,19,1,1,18,-1,3,17,1,18,-1,19,-1,2,
138,1,140,1,1,139,-1,2,138,1,139,1,4,137,-1,138,1,139,1,
140,1,1,36,-1,2,33,-1,35,1,4,33,1,34,-1,35,-1,36,-1,
2,33,1,36,-1,2,105,-1,108,1,2,106,1,108,1,1,106,-1,2,
105,-1,107,1,2,155,1,156,-1,4,153,-1,154,1,155,1,156,1,
2,154,-1,156,-1,3,153,1,154,-1,156,-1,1,68,-1,2,65,-1,
67,1,4,65,1,66,-1,67,-1,68,-1,2,65,1,68,-1,2,146,-1,
147,-1,3,145,1,146,-1,148,-1,2,147,-1,148,1,1,147,-1,
1,13,1,1,14,1,1,15,1,1,16,1,2,69,1,71,-1,1,72,-1,
1,69,1,2,70,1,72,1,1,136,-1,2,134,-1,135,-1,3,133,-1,
134,1,135,1,1,134,1,2,42,1,43,1,1,44,-1,2,42,1,44,1,
1,41,1,1,58,-1,4,57,-1,58,1,59,1,60,1,3,57,1,58,-1,
60,-1,2,58,-1,60,-1,1,51,-1,3,49,1,50,-1,51,-1,1,49,-1,
3,49,-1,50,1,52,1,2,10,1,12,1,1,11,-1,2,10,1,11,1,4,
9,-1,10,1,11,1,12,1,2,98,-1,99,-1,3,97,1,98,-1,100,-1,
2,99,-1,100,1,1,99,-1,1,29,1,1,30,1,1,31,1,1,32,1,2,
26,-1,28,-1,2,25,-1,28,1,2,27,1,28,-1,1,28,-1,2,61,1,
63,-1,1,64,-1,1,61,1,2,62,1,64,1,2,149,-1,152,1,2,
150,1,152,1,1,150,-1,2,149,-1,151,1,1,90,-1,4,89,-1,
90,1,91,1,92,1,3,89,1,90,-1,92,-1,2,90,-1,92,-1,1,
47,-1,3,45,1,46,-1,47,-1,1,45,-1,3,45,-1,46,1,48,1,
2,75,1,76,-1,4,73,-1,74,1,75,1,76,1,2,74,-1,76,-1,3,
73,1,74,-1,76,-1,3,157,-1,158,1,160,1,2,158,-1,159,-1,
1,158,1,3,157,-1,158,1,159,1,1,109,1,1,110,1,1,111,1,
1,112,1,2,93,1,95,-1,1,96,-1,1,93,1,2,94,1,96,1,2,
7,-1,8,1,1,5,1,2,6,-1,7,-1,2,5,-1,8,1,2,77,-1,80,1,
3,77,1,78,-1,79,-1,3,77,-1,78,1,80,1,1,77,-1,2,102,-1,
104,-1,2,101,-1,104,1,2,103,1,104,-1,1,104,-1,1,38,-1,
4,37,-1,38,1,39,1,40,1,3,37,1,38,-1,40,-1,2,38,-1,
40,-1,1,21,1,1,22,1,1,23,1,1,24,1,2,87,1,88,-1,4,
85,-1,86,1,87,1,88,1,2,86,-1,88,-1,3,85,1,86,-1,88,-1,
1,131,1,2,130,1,132,1,2,129,-1,131,1,1,130,-1
]))>;

return _LR;
