//Standard generators of L2(17) are a and b where a has order 2, b has order 3
//and ab has order 17.
//Standard generators of the double cover 2.L2(17) = SL2(17) are preimages A and
//B where B has order 3 and AB has order 17.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [a^-1, (b*a)^3*(b^-1*a*b*a)^2] ]
             where a is (_LR`F).1 where b is (_LR`F).2;
//one constituent fixed by _LR`AI[1][1]
_LR`G :=
MatrixGroup<16, ext<K|Polynomial(K, [1, 0, 1])> where K is RationalField() |
[[-7,-7],[0,-3],[
-2,1],[4,8],[
-5,-14],[-4,-2],[-9,-6],[
9,-1],[4,7],[
10,2],[3,1],[-2,-4],[
-5,-8],[4,-4],[
-2,-10],[-2,-6],[11,2],[
2,2],[3,-1],[
-7,-4],[11,11],[4,1],[
9,3],[-6,5],[
-6,-4],[-9,3],[-2,1],[
4,2],[8,6],[
-1,3],[7,8],[4,4],[
-9,7],[-3,0],[
-2,2],[7,-3],[-15,1],[
-3,2],[-8,5],[
0,-8],[7,-2],[3,-9],[
1,-3],[-5,2],[
-10,1],[-2,-2],[-11,0],[
-6,0],[3,-3],[
1,-1],[1,0],[-1,3],[
3,-1],[0,1],[
1,1],[2,2],[-1,0],[
1,2],[0,0],[1,
-2],[2,0],[1,-2],[
3,0],[1,0],[
-1,-5],[1,-1],[-1,-1],[
0,4],[2,-7],[
-1,-2],[-1,-4],[4,2],[
0,3],[4,3],[1,
1],[0,-3],[1,-5],[
2,-1],[2,-5],[
1,-3],[1,-11],[2,-2],[
-1,-3],[-3,8],[
9,-13],[0,-4],[1,-9],[
6,6],[-3,6],[
5,9],[1,2],[2,-5],[
5,-8],[4,0],[
7,-8],[4,-5],[7,-3],[
2,1],[1,-2],[
-7,0],[12,1],[3,-2],[
7,-5],[-3,6],[
-6,1],[-5,7],[-1,2],[
4,0],[8,0],[1,
4],[8,2],[5,1],[
0,2],[0,0],[
-1,0],[-1,-1],[-1,1],[
-1,0],[-1,-1],[
-1,1],[0,0],[0,-1],[
0,0],[0,1],[
-1,0],[1,1],[-1,1],[
0,0],[1,-6],[
2,-1],[-1,-2],[-4,4],[
7,-8],[0,-4],[
0,-8],[2,5],[-2,5],[
2,7],[2,2],[2,
-2],[4,-6],[3,2],[
5,-5],[3,-3],[
-1,-6],[1,-1],[-1,-1],[
-1,5],[4,-9],[
-1,-3],[-1,-7],[4,3],[
-1,5],[4,5],[
1,2],[1,-3],[2,-6],[
3,0],[3,-6],[
2,-4],[5,-2],[1,0],[
1,-1],[-4,1],[
7,1],[1,0],[4,-2],[
-1,4],[-4,0],[
-2,4],[-1,1],[3,-1],[
5,1],[1,1],[5,
2],[3,1],[11,5],[
1,3],[4,0],[
-5,-6],[9,15],[5,2],[
11,6],[-8,3],[
-6,-6],[-12,1],[-4,0],[
4,4],[7,10],[
-3,3],[5,11],[3,6],[
-11,-2],[-2,-3],[
-3,1],[7,5],[-13,-12],[
-5,1],[-13,-1],[
8,-5],[8,4],[11,-5],[
4,-2],[-5,-3],[
-10,-7],[2,-5],[-8,-9],[
-5,-5],[-4,-3],[
-1,-2],[-1,0],[3,4],[
-5,-7],[-2,2],[
-6,1],[5,-2],[4,1],[
6,-2],[2,-2],[
-2,-3],[-4,-3],[1,-4],[
-2,-4],[-2,-2],[
7,2],[1,2],[1,0],[
-5,-3],[8,7],[
3,0],[7,0],[-5,4],[
-5,-2],[-7,3],[
-2,1],[3,2],[6,3],[
-1,4],[5,6],[
3,3],[3,7],[-1,1],[
2,1],[0,-6],[
-2,13],[2,3],[4,8],[
-6,-3],[-1,-6],[
-7,-6],[-2,-1],[0,4],[
0,9],[-4,0],[
-2,8],[-1,5]],
[[3,10],[-1,2],[
2,3],[1,-6],[
-6,13],[0,4],[1,9],[
-6,-3],[2,-7],[
-6,-7],[-1,-2],[1,4],[
-4,10],[-2,-1],[
-4,9],[-3,5],[-5,5],[
-2,0],[-1,1],[
4,-3],[-9,3],[-1,1],[
-4,4],[-1,-5],[
4,-2],[1,-6],[0,-1],[
-3,2],[-5,2],[
-2,-1],[-6,1],[-3,1],[
2,1],[1,0],[
-1,0],[-3,0],[2,1],[
-1,0],[-1,-1],[
-1,2],[-1,0],[0,1],[
0,0],[1,0],[1,
0],[2,1],[1,1],[
1,0],[-3,4],[
-2,0],[1,2],[4,-3],[
-7,5],[0,2],[
-1,6],[-1,-5],[3,-3],[
-1,-6],[0,-1],[
-2,2],[-4,4],[-3,-2],[
-5,2],[-3,2],[
-1,2],[-1,1],[1,0],[
1,-3],[-1,3],[
1,0],[2,1],[-2,-2],[
0,-1],[-2,-1],[
-1,0],[0,2],[0,2],[
-2,1],[-1,2],[
0,2],[-2,-1],[-1,-1],[
0,1],[3,1],[
-3,-1],[0,1],[0,2],[
2,-2],[1,0],[
1,-2],[0,-1],[-1,0],[
-2,0],[-1,-2],[
-2,-1],[-2,0],[2,-1],[
1,0],[0,0],[
-2,1],[3,-1],[1,-1],[
1,-1],[0,2],[
-1,1],[-1,2],[0,1],[
1,0],[1,-1],[
1,1],[2,0],[1,-1],[
-10,2],[-2,-1],[
-3,1],[6,1],[-12,-7],[
-4,-1],[-9,-2],[
3,-5],[6,3],[7,-4],[
2,-1],[-4,0],[
-8,-5],[1,-1],[-8,-5],[
-4,-3],[6,4],[
1,2],[1,0],[-4,-4],[
5,8],[2,-1],[
6,1],[-6,3],[-4,-3],[
-7,2],[-2,1],[
3,3],[4,5],[-1,4],[
3,6],[2,3],[
-1,2],[-1,1],[1,0],[
2,-3],[-2,4],[
2,1],[3,3],[-2,-3],[
0,-2],[-3,-3],[
-1,-1],[-1,2],[-1,3],[
-3,0],[-2,2],[
-1,2],[-11,-5],[-2,-3],[
-2,1],[8,6],[
-11,-13],[-3,0],[-10,-2],[
9,-5],[7,5],[
11,-3],[3,-1],[-5,-4],[
-8,-8],[1,-5],[
-6,-10],[-4,-5],[-3,9],[
-2,1],[0,2],[
5,-6],[-11,11],[1,4],[
0,11],[-4,-7],[
3,-7],[-4,-11],[-2,-4],[
-4,5],[-6,8],[
-5,-2],[-9,6],[-5,4],[
2,11],[-1,3],[
0,2],[0,-8],[-5,14],[
0,3],[2,8],[
-8,-3],[0,-7],[-7,-6],[
-2,-2],[0,5],[
-2,9],[-3,2],[-5,9],[
-2,5],[6,-1],[
1,0],[1,1],[-4,1],[
6,2],[0,1],[1,
1],[0,4],[-2,0],[
-2,3],[0,1],[
3,-1],[3,1],[2,0],[
4,2],[2,0],[
-5,-7],[1,-2],[-2,-2],[
0,6],[1,-14],[
-3,-4],[-6,-9],[6,2],[
2,7],[9,5],[3,
2],[-1,-4],[-1,-10],[
4,0],[1,-9],[
1,-6],[-6,-2],[-1,-1],[
-1,0],[4,2],[
-6,-6],[-1,-1],[-5,-1],[
4,-3],[4,2],[
5,-2],[2,0],[-3,-2],[
-4,-4],[0,-2],[
-3,-6],[-2,-3]]>;

return _LR;
