_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [ a^-1, b ] ]
                     where a is (_LR`F).1 where b is (_LR`F).2;
//Standard generators of A11 are a and b where a is in class 3A, b has order 9,
//ab has order 11.  Standard generators of the double
//cover 2.A11 are preimages A and B where A has order 3 and B has order 9.
//Two components, interchanged by _LR`AI[1].

_LR`G :=
MatrixGroup<16, ext<K|Polynomial(K, [3, 1, 1])> where K is RationalField() |
[[-12,15],[30,7],[
36,2],[21,-13],[
-14,7],[-3,2],[6,-10],[
11,18],[-16,7],[
-2,-11],[-9,8],[4,-10],[
-13,-7],[10,16],[
-3,12],[-16,6],[35,32],[
31,-20],[22,-30],[
-29,-39],[12,21],[
4,5],[-23,-19],[
54,15],[11,23],[-33,-11],[
18,19],[-24,-18],[
-27,3],[58,16],[
44,22],[4,28],[16,-8],[
-23,-7],[-28,-6],[
-22,8],[12,-1],[
3,-1],[-11,4],[1,-13],[
14,-2],[-1,7],[
11,-4],[-9,5],[8,6],[
-7,-15],[0,-12],[
21,-3],[-9,-8],[-8,5],[
-6,8],[7,10],[
-2,-5],[-1,-1],[5,5],[
-14,-4],[-3,-6],[
8,3],[-4,-5],[6,5],[
7,0],[-14,-5],[
-11,-6],[0,-7],[-20,-21],[
-24,11],[-18,17],[
13,25],[-8,-14],[
-4,-4],[15,12],[-33,-11],[
-5,-15],[22,9],[
-11,-12],[14,11],[17,-1],[
-36,-11],[-25,-15],[
1,-16],[3,-11],[
-18,-3],[-21,1],[-9,9],[
7,-7],[0,-2],[
1,8],[-12,-11],[8,-6],[
5,8],[2,-6],[
1,7],[10,4],[-6,-10],[
2,-8],[9,-3],[
10,4],[1,-6],[-1,-7],[
-10,-6],[5,4],[
3,0],[-7,-2],[11,1],[
6,4],[-9,-1],[
6,2],[-6,-2],[-3,1],[
7,-1],[6,1],[
3,4],[20,22],[24,-12],[
18,-18],[-15,-26],[
6,14],[3,4],[
-14,-13],[34,12],[5,15],[
-22,-9],[11,13],[
-14,-12],[-18,1],[38,12],[
28,16],[-1,17],[
-12,-7],[-9,5],[-3,9],[
7,9],[-6,-6],[
-2,-2],[8,4],[-13,-2],[
-6,-7],[8,4],[
-6,-5],[9,4],[5,-1],[
-11,-3],[-7,-5],[
-2,-4],[19,-3],[-19,-13],[
-24,-10],[-29,-1],[
14,-1],[3,-1],[
-10,3],[7,-10],[16,0],[
-8,8],[12,-2],[
-9,3],[3,7],[13,-10],[
20,-5],[18,7],[
-3,8],[12,0],[14,-1],[
4,-8],[-5,5],[
1,1],[-1,-6],[10,9],[
-5,4],[-8,-6],[
0,4],[0,-5],[-8,-3],[
8,7],[2,6],[
-8,4],[14,-5],[-17,-8],[
-21,-6],[-20,3],[
11,-2],[2,-1],[-7,4],[
1,-10],[12,-1],[
-2,7],[8,-3],[-7,4],[
5,6],[5,-10],[
11,-7],[16,3],[-1,5],[
10,1],[10,-1],[
5,-5],[-2,3],[0,1],[
0,-3],[5,5],[
-3,3],[-3,-4],[-1,3],[
0,-3],[-5,-2],[
3,5],[0,5],[-6,1],[
-4,0],[4,2],[
4,2],[6,0],[-2,0],[
0,0],[2,0],[
-2,2],[-2,0],[0,-2],[
-2,0],[2,0],[
0,-2],[-3,3],[-4,2],[
-6,-2],[2,0],[
-2,-1],[-2,-1],[-3,0],[
1,0],[0,0],[
-1,0],[1,-1],[1,0],[
0,1],[1,0],[
-1,0],[0,1],[-1,-2],[
0,-1],[3,0],[
0,-2],[-3,1],[-3,1],[
0,3],[0,-1],[
0,0],[0,1],[-3,-2],[
0,-1],[3,1],[
0,-1],[0,1],[3,1],[
-5,-4],[-4,-4],[
4,-2]],
[[-40,-48],[-62,19],[
-48,39],[21,55],[
-8,-34],[-5,-8],[30,31],[
-76,-29],[-8,-36],[
46,26],[-20,-30],[
32,29],[41,3],[
-66,-30],[-38,-35],[7,-30],[
-65,-41],[-26,35],[
-15,49],[62,50],[
-20,-28],[-11,-5],[38,25],[
-81,-15],[-27,-33],[
47,12],[-33,-24],[
40,24],[28,-7],[
-72,-5],[-60,-16],[-28,-38],
[-11,18],[37,10],[
45,2],[26,-15],[
-17,9],[-1,3],[6,-12],[
13,21],[-19,10],[
-1,-15],[-10,10],[4,-12],[
-13,-8],[4,18],[
-10,13],[-20,3],[-37,6],[
29,20],[45,20],[
45,-1],[-30,-4],[-5,1],[
25,-4],[-15,20],[
-30,-2],[15,-11],[-24,2],[
24,-5],[-2,-11],[
-12,16],[-20,8],[-29,-5],[
86,6],[-36,-46],[
-65,-51],[-98,-19],[55,15],
[14,1],[-52,-2],[
53,-26],[59,17],[
-40,12],[51,6],[-51,0],[
-4,22],[47,-27],[
57,-9],[62,23],[-56,-11],[
9,30],[28,36],[
60,21],[-33,-13],[-9,-1],[
33,5],[-42,10],[
-37,-16],[31,-3],[-31,-8],[
33,5],[7,-12],[
-38,9],[-40,-2],[-31,-18],[
9,6],[3,-5],[
3,-7],[-8,-7],[0,4],[
1,1],[-5,-4],[
12,3],[4,4],[-6,-2],[
4,4],[-5,-4],[
-4,0],[9,0],[8,1],[
4,5],[-58,-14],[
11,32],[28,37],[64,23],[
-34,-15],[-10,-2],[
36,7],[-47,9],[
-35,-16],[33,-4],[-34,-9],[
36,6],[11,-13],[
-46,10],[-47,-2],[-35,-23],
[14,-14],[-30,-3],[
-35,-2],[-17,16],[
14,-3],[1,-1],[
-10,8],[-8,-19],[13,-6],[
7,10],[9,-7],[
-9,9],[11,7],[-17,-18],[
-8,-16],[23,-8],[
-25,5],[23,15],[30,13],[
34,-1],[-17,1],[
-4,2],[13,-4],[-8,13],[
-22,-1],[9,-9],[
-14,3],[12,-4],[-6,-8],[
-8,15],[-17,9],[
-24,-5],[-22,-12],[-4,16],[
3,17],[27,17],[
-13,-8],[-4,-1],[14,6],[
-26,-2],[-12,-9],[
21,0],[-14,-6],[
14,6],[11,-4],[-35,-2],[
-32,-8],[-9,-17],[
1,-8],[-16,-3],[
-17,2],[-8,7],[6,-5],[
1,-1],[0,6],[
-8,-8],[5,-6],[3,7],[
3,-5],[1,6],[
6,3],[-1,-7],[5,-5],[
6,-1],[25,28],[
35,-14],[27,-24],[-17,-34],[
5,18],[4,4],[
-16,-17],[44,17],[7,21],[
-29,-14],[12,17],[
-17,-17],[-22,-1],[
43,16],[29,20],[
-3,20],[16,20],[21,-11],[
19,-16],[-14,-24],[
2,12],[3,2],[
-10,-12],[33,13],[4,13],[
-21,-8],[8,11],[
-10,-12],[-16,-1],[32,11],[
24,14],[-3,16],[
-7,5],[14,7],[17,3],[
15,-2],[-8,3],[
-2,1],[3,-4],[1,7],[
-9,3],[3,-6],[
-6,3],[2,-4],[-4,-4],[
-5,6],[-11,3],[
-7,-2],[-31,4],[23,16],[
35,17],[37,0],[
-23,-3],[-3,1],[19,-3],[
-13,16],[-24,-2],[
10,-9],[-18,1],[
19,-3],[-2,-9],[-10,13],[
-17,7],[-25,-5]]>;

return _LR;
