//Standard generators of L2(37) are a and b where a has order 2, b has order 3
//and ab has order 37.
//Standard generators of the double cover 2.L2(37) = SL2(37) are preimages A and
//B where B has order 3 and AB has order 37.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI:=[[a^-1, a^-1*b*a*b^-1*a*b*a*b^-1*a^-1*b*a*b*a*b^-1*a^-1*b^-1*a*b^-1*a*
                             b*a*b^-1*a^-1*b*a*b*a*b^-1*a^-1*b*a^-1*b^-1*a*b]]
             where a is (_LR`F).1 where b is (_LR`F).2;
//nine constituents
_LR`G :=
/*
Original group: c9Group("l237p")
Direct integral method
Schur index: 1
Character: ( 324, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, -9, -9 )
*/

MatrixGroup<324,IntegerRing() |
Matrix(324,324,\[-18,-30,-29,-26,5,12,-45,-8,2,5,18,22,
12,3,-7,-24,22,4,-12,-11,11,16,-3,17,34,37,52,-21,
-19,49,-3,-7,9,-14,10,33,3,-34,-3,22,39,-15,5,-13,
-15,-6,-7,12,-9,8,14,-14,-18,-1,-6,9,1,10,1,-10,8,
-13,18,9,1,-10,-1,0,11,7,-4,6,-4,1,-3,-1,-6,0,-3,
1,-10,-2,0,0,0,-15,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
2,0,0,0,0,0,0,0,-8,0,0,0,0,0,0,0,0,0,0,0,0,1,
0,4,5,0,0,0,0,0,0,0,0,0,0,0,7,0,0,0,0,-7,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,5,0,0,0,0,0,0,12,-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,
0,0,0,0,0,0,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
6,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,
0,0,-19,5,21,18,12,14,-20,-15,13,1,-6,-2,-23,7,3,
-1,-4,3,-19,27,-14,27,-13,-5,-23,8,-26,1,9,-2,7,-8,
7,1,11,-21,18,-7,-3,-16,-9,-4,3,4,-33,-8,-8,3,-17,
4,0,7,1,-14,7,-15,-8,4,-4,-2,1,-5,2,11,3,-8,-8,3,
2,-7,5,0,-10,2,-4,-4,-2,0,-5,-1,3,-10,0,-4,0,10,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,3,0,0,0,0,0,
0,0,0,0,0,0,-2,0,0,0,0,5,0,0,0,0,0,0,-1,0,0,0,
0,0,0,0,0,3,0,0,0,0,0,0,-1,-2,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,-1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-9,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-21,-18,-8,-20,
16,-26,23,-30,5,0,0,-6,-4,-2,12,-9,-24,45,15,-19,25,
1,-18,2,9,-11,27,30,12,-10,-13,-10,2,-1,25,-29,-12,
-10,0,4,-19,10,5,-9,8,10,12,4,3,4,-2,30,-4,11,26,
-12,-1,-1,15,1,1,9,11,-2,4,3,3,-10,7,-17,-4,5,-8,
0,-6,7,-7,0,-9,6,-1,7,0,-2,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,-3,0,0,0,0,0,0,0,-5,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,-3,0,0,0,0,0,0,0,0,0,0,0,-5,0,
0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,8,0,0,0,-1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,5,0,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,-13,17,-13,-3,-10,26,-28,11,
15,-16,7,-4,0,23,14,-43,38,-17,-20,-15,5,25,4,-9,
-7,14,-16,-10,-25,12,-6,5,-3,-22,-4,14,11,1,-19,2,
41,7,3,8,-23,3,9,16,-13,-2,9,-10,-10,7,-15,13,-7,
-8,12,22,10,4,10,-3,5,1,5,-7,8,2,0,-2,-1,-2,-8,6,
-9,0,-6,12,-3,11,0,-4,0,-12,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,-1,0,0,0,0,0,0,0,-5,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,2,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,-4,0,0,0,0,
0,0,5,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,6,0,0,0,6,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,3,0,0,0,0,0,-5,-17,3,9,-8,12,-16,-3,5,-18,-8,
20,-1,10,3,-5,-2,3,-7,-6,-17,-12,-25,-16,6,14,-13,
-5,-1,23,22,6,-10,-3,-6,-11,9,-15,-5,-25,3,-5,-1,2,
-25,1,-5,14,-8,4,-4,2,-2,-9,-1,-4,3,9,3,-10,1,-13,
10,6,4,-8,-6,4,-1,-6,-3,0,-5,4,3,-4,3,0,0,-6,-3,
-9,0,1,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,0,0,
0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,5,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,0,0,0,0,
0,-1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,-2,0,0,
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,
0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-2,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,
0,0,-11,6,18,19,4,6,-29,-23,0,-13,4,4,-12,8,-1,7,
-11,-3,-21,26,-19,2,-13,-14,-21,17,-17,-18,-5,0,11,
-3,4,-10,-7,-14,16,3,-4,-25,10,-10,1,-4,-31,-7,-12,
4,-3,1,5,-11,-6,-10,0,0,-6,0,-3,-7,8,-9,-1,9,3,
-9,0,5,-4,4,6,-5,0,6,9,-1,-5,0,-4,1,1,-10,0,-2,
0,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,0,0,0,0,0,
0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,1,0,0,0,
0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,4,0,0,0,0,0,0,6,0,0,0,0,0,0,0,
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,
0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,2,19,
-1,0,-8,8,-2,8,7,-11,25,-1,1,-4,12,-18,40,-11,2,4,
11,18,29,-1,-17,-11,-28,1,4,-22,-17,-3,-1,-2,-6,10,
1,22,-5,2,15,6,3,-1,13,-1,11,3,3,-17,7,4,6,6,6,
-9,2,-6,6,16,1,14,-8,-7,12,8,-5,-4,-6,6,6,-8,-4,
-2,-7,7,0,0,-5,-2,-1,4,0,-7,0,6,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,-5,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,-3,-5,0,0,0,0,0,0,0,0,0,0,0,1,0,
0,0,0,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,
0,0,0,0,-4,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,3,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,-3,0,0,0,0,0,9,-2,5,10,0,1,10,1,-6,-3,-1,1,
-10,-14,-2,9,3,-8,12,7,-2,-3,0,7,-16,-4,-9,-1,10,
-7,1,2,-4,1,-9,8,-4,1,1,-7,9,-6,6,-1,14,1,3,-3,
4,-5,2,0,8,-6,5,-8,10,-1,-2,5,-4,9,0,3,6,3,-1,
-4,0,2,-1,-2,6,5,1,0,-1,0,-6,-3,1,-1,0,3,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,6,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-4,0,0,0,0,0,0,
0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,1,0,0,0,0,0,0,-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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,
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,-4,0,0,0,0,0,9,-1,-11,-21,-5,
2,10,0,4,16,-17,-31,15,-1,3,-12,9,-17,-3,-17,11,-2,
4,2,4,-9,18,2,8,-12,10,17,-13,-14,-8,-4,5,15,-14,
9,15,0,8,8,-25,-6,-10,-12,-18,2,-5,8,8,-15,-2,-9,
-4,-12,3,11,-4,-2,13,2,-8,5,5,1,3,-5,-2,0,3,-4,4,
4,-1,0,-2,10,11,2,0,-2,0,6,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,-1,0,0,0,0,2,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,-1,6,0,0,0,0,0,0,0,0,0,0,0,-7,0,0,0,
0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,-5,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,-1,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
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,
0,0,3,0,0,0,0,0,2,32,1,21,2,17,-5,49,-8,32,-26,
-24,-11,16,3,-9,18,-15,-2,-4,-1,41,2,7,2,-21,-9,16,
4,-15,-10,11,8,11,2,-10,4,-5,-3,3,-41,6,-10,6,-15,
2,-3,3,-10,0,-7,-3,8,3,-11,-4,-4,-6,-11,6,-4,7,-4,
4,-10,-1,2,-1,10,-3,-5,7,-2,-8,-6,-10,-2,0,3,2,-1,
-3,0,-3,0,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,
0,0,0,0,0,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,5,
0,0,0,0,0,0,0,0,0,0,0,-5,0,0,0,0,2,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,-2,0,0,0,0,0,0,-3,1,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,
0,0,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,0,0,0,0,
-19,-6,-31,-13,-10,-4,19,19,5,-7,-14,-16,25,14,6,-25,
14,19,23,-41,37,-7,-10,18,34,-7,14,26,-13,-9,-9,8,2,
-12,9,8,-15,-5,-6,7,-11,-2,6,-5,25,11,22,29,-11,0,
13,6,-1,18,0,6,4,-8,12,18,7,22,12,-16,8,10,10,-23,
16,1,-5,-1,-7,-6,-15,10,-7,0,-6,8,-13,13,0,5,0,-7,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,-12,0,0,0,0,0,0,0,
-7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-7,0,0,0,0,
0,0,0,0,0,0,0,-1,0,0,0,0,4,0,0,0,0,0,0,2,0,0,
0,0,0,0,0,0,-7,0,0,0,0,0,0,6,2,0,0,0,0,0,0,0,
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,
0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,3,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,0,0,0,
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,-3,0,0,0,0,0,-9,17,
-1,16,-9,-12,-6,4,-2,-1,-23,-8,-11,12,4,-10,-1,10,
-9,-7,13,-1,-7,6,6,-9,-8,28,-3,-5,8,8,-2,-2,9,-20,
15,-1,-10,-15,-26,-1,-8,8,-13,-1,-7,15,-8,-2,6,4,9,
-6,-6,-14,-4,4,-4,11,3,-1,-4,-5,-1,5,3,-5,9,-2,4,
-1,-11,-3,-4,0,1,0,-1,-1,-6,-6,0,-2,0,7,0,0,0,0,
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30,-9,-8,19,3,32,-3,31,-14,-12,-12,10,17,12,-1,0,3,
30,-7,0,2,-8,0,-8,0,0,0,0,0,0,0,0,-3,0,0,0,0,0,
0,8,0,0,-6,-8,0,0,0,0,0,14,0,0,0,-2,0,0,0,0,12,
0,8,0,0,0,4,4,5,0,0,0,0,0,3,2,0,0,0,0,15,0,0,
0,0,0,-20,0,0,2,11,10,0,3,0,0,0,0,0,0,0,0,0,0,
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14,0,0,0,0,0,0,-3,0,0,0,-6,1,0,0,0,0,0,0,0,0,
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7,35,11,8,9,55,-18,3,20,2,23,23,14,11,15,-7,-1,23,
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6,-3,-41,18,2,-37,-44,10,-20,0,-14,-25,12,1,-10,37,
22,-17,1,24,-28,-17,1,-13,0,-27,19,-3,15,3,1,0,-11,
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-3,3,6,0,5,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,0,0,0,-5,0,0,0,0,0,0,0,0,0,-7,0,0,0,0,0,0,
1,0,0,0,9,-12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-17,0,0,0,0,
0,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,6,
-9,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0])>;

return _LR;
