//Standard generators of L2(23) are a, b where a has order 2,
//b has order 3 and ab has order 23.
//Standard generators of 2.L2(23) = SL2(23) are preimages A, B where
//B has order 3 and AB has order 23. 
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [a^-1, b^-1] ]
             where a is (_LR`F).1 where b is (_LR`F).2;
//two constituents interchanged by _LR`AI[1][1]
_LR`G :=
MatrixGroup<11, ext<K|Polynomial(K, [6, -1, 1])> where K is RationalField() |
[[346,26],[26,-155],[
23,65],[-165,-8],[
-88,75],[-29,150],[
22,22],[-81,88],[
145,-136],[17,38],[-186,98],
[104,45],[98,-65],[
-29,31],[-51,-20],[
-76,25],[-95,63],[
-5,11],[-77,31],[
128,-46],[-16,18],[-121,25],
[1,21],[53,-11],[
-20,6],[-2,-10],[
-27,2],[-50,10],[-8,3],[
-30,2],[48,-3],[
-13,4],[-38,-2],[14,6],[
13,-8],[-3,4],[
-6,-3],[-11,4],[-12,8],[
-1,1],[-9,4],[
17,-6],[-2,2],[-16,3],[
-51,70],[177,-15],[
-76,13],[20,-33],[
-82,-7],[-171,14],[
-27,7],[-96,-4],[
148,10],[-45,8],[-102,-23],
[171,-18],[-63,-61],[
40,23],[-80,10],[
-5,36],[60,59],[21,6],[
6,40],[0,-63],[
27,13],[-36,52],[24,42],[
100,-31],[-37,17],[
-14,-19],[-58,7],[
-97,30],[-12,7],[
-64,11],[102,-15],[-22,10],
[-84,2],[-51,10],[
29,16],[-16,-5],[
24,-5],[-5,-11],[-29,-15],[
-7,-1],[-9,-11],[
11,18],[-11,-3],[3,-16],[
81,-117],[-297,27],[
126,-22],[-30,55],[
136,11],[286,-25],[
45,-12],[162,6],[
-249,-15],[75,-14],[174,37],
[-171,24],[77,58],[
-47,-21],[80,-13],[
-4,-35],[-73,-56],[
-22,-6],[-14,-39],[
13,62],[-30,-12],[
27,-53],[67,40],[
91,-48],[-30,23],[-34,-18],
[-62,17],[-88,46],[
-7,9],[-66,21],[
108,-31],[-17,14],[-97,15]
],
[[-353,7],[52,141],[
-56,-55],[167,-7],[
48,-75],[-49,-136],[
-31,-18],[34,-85],[
-71,134],[-35,-33],[
132,-105],[-376,43],[
146,132],[-94,-49],[
175,-24],[6,-78],[
-138,-128],[-46,-14],[
-17,-87],[7,138],[
-60,-28],[76,-115],[
0,0],[0,0],[0,
0],[0,0],[0,0],[
0,0],[-1,0],[
0,0],[0,0],[0,0],[
0,0],[-92,52],[
137,11],[-64,1],[40,-25],[
-52,-17],[-132,-11],[
-24,2],[-65,-16],[
97,28],[-38,1],[
-54,-33],[-116,-63],[-143,80
],[46,-38],[59,28],[
99,-28],[139,-77],[
10,-15],[107,-36],[
-173,53],[26,-23],[
158,-27],[37,-32],[
-81,1],[36,-4],[
-16,15],[36,6],[78,-1],[
13,-2],[41,5],[
-64,-10],[21,-2],[41,15],[
-120,-2],[6,50],[
-15,-20],[57,0],[21,-26],[
-6,-48],[-8,-7],[
18,-29],[-34,46],[-9,-12],[
53,-35],[-148,34],[
99,43],[-54,-14],[
68,-17],[-20,-30],[
-95,-42],[-23,-3],[
-32,-32],[42,52],[
-33,-8],[0,-47],[
-36,-23],[-52,27],[18,-13],
[18,10],[36,-9],[
51,-26],[3,-5],[
38,-12],[-62,17],[9,-8],[
54,-8],[-170,-93],[
-211,118],[69,-56],[
87,41],[146,-41],[
205,-113],[15,-22],[
158,-53],[-255,78],[
38,-34],[233,-40],[
-102,-7],[-5,45],[
-8,-19],[48,2],[
27,-22],[6,-44],[-8,-6],[
22,-26],[-41,40],[
-6,-11],[53,-29]]>;

return _LR;
