//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 both fixed by _LR`AI[1][1]
_LR`G :=
MatrixGroup<22, ext<K|Polynomial(K, [-3, 0, 1])> where K is RationalField() |
[[-40,-19],[294,188],[
-50,-23],[392,232],[
-288,-179],[205,120],[
101,52],[478,265],[
686,393],[-364,-202],[
-184,-108],[-44,-29],[
86,43],[-22,-23],[
603,354],[136,74],[
64,53],[-292,-158],[
-145,-63],[-15,1],[
666,386],[786,450],[
58,26],[73,45],[
-11,-15],[-10,-6],[-146,-82
],[-75,-48],[-209,-123],[
8,5],[5,-6],[
-74,-45],[-40,-15],[33,24],[
1,-9],[24,15],[
-32,-10],[82,47],[7,-1],[
1,4],[-54,-30],[
-4,8],[67,41],[81,49],[
3,0],[185,102],[
-28,-18],[197,112],[-205,-115
],[78,44],[-30,-15],[
236,139],[340,197],[
-202,-120],[-104,-59],[
-9,-4],[38,23],[
-11,-3],[296,170],[95,56],[
43,20],[-136,-81],[
-77,-50],[1,-1],[
360,208],[421,244],[55,33],
[-191,-113],[22,14],[
-306,-177],[147,86],[
-202,-116],[-188,-107],[
-353,-202],[-518,-297],[
231,133],[126,71],[
56,32],[-69,-37],[
35,21],[-472,-275],[
-56,-32],[-58,-34],[
218,124],[69,37],[
11,3],[-468,-271],[
-547,-316],[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],[
37,33],[-8,-4],[48,30],[
-47,-33],[20,11],[
-4,-7],[67,32],[
91,48],[-57,-29],[-29,-15],
[-2,-2],[15,3],[
4,-4],[70,47],[27,13],[
4,10],[-43,-17],[
-32,-6],[-8,4],[91,54],[
109,62],[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],[37,33],[
-8,-4],[50,32],[
-48,-34],[23,13],[-1,-6],[
70,34],[95,50],[
-57,-29],[-29,-15],[-2,-2],
[15,3],[4,-4],[
74,49],[27,13],[4,10],[
-43,-17],[-32,-6],[
-8,4],[95,56],[
113,64],[0,0],[37,33],[
-8,-4],[49,31],[
-47,-33],[21,12],[-1,-6],[
68,33],[94,49],[
-57,-29],[-29,-15],[-2,-2],
[15,3],[4,-4],[
72,48],[27,13],[4,10],[
-43,-17],[-32,-6],[
-8,4],[93,55],[
111,63],[-8,-4],[39,27],[
-7,-3],[59,35],[
-37,-24],[34,20],[24,12],[
72,39],[103,58],[
-51,-28],[-26,-15],[-7,-5],
[14,7],[-4,-5],[
90,54],[17,9],[8,8],[
-45,-23],[-21,-7],[
-3,1],[97,56],[
114,65],[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],[0,0],[0,
0],[0,0],[0,0],[
25,13],[-29,-21],[
4,0],[-74,-44],[
4,6],[-61,-36],[-86,-49],[
-84,-46],[-125,-72],[
43,23],[23,14],[
20,13],[-17,-9],[11,9],[
-118,-69],[2,2],[
-10,-10],[56,30],[11,1],[
5,1],[-98,-57],[
-117,-66],[-14,-8],[35,15],
[-3,-2],[59,33],[
-21,-9],[43,25],[
48,29],[62,39],[96,57],[
-36,-22],[-19,-12],[
-13,-7],[10,9],[
-11,-4],[93,51],[3,3],[
13,4],[-38,-25],[
-4,-8],[2,-3],[84,47],[
96,56],[-12,-6],[
15,8],[-1,0],[33,19],[
-3,-1],[27,16],[
40,22],[36,21],[55,32],[
-19,-10],[-10,-7],[
-11,-6],[5,5],[
-4,-3],[53,30],[-2,-1],[
7,4],[-24,-14],[
-2,-2],[-1,-2],[44,24],[
50,29],[-29,-15],[
193,110],[-29,-15],[
255,147],[-179,-103],[
138,81],[79,46],[
299,173],[435,253],[-223,-128
],[-114,-68],[-32,-19],[
50,32],[-22,-13],[
393,225],[78,45],[
49,29],[-180,-105],[
-75,-45],[-2,-4],[
422,243],[494,285],[
-21,-13],[123,67],[
-15,-11],[169,97],[
-109,-60],[99,57],[
68,40],[194,115],[
287,166],[-139,-81],[
-73,-42],[-25,-13],[
35,21],[-19,-9],[
260,149],[45,26],[35,17],[
-116,-70],[-41,-29],[
-1,-3],[272,157],[
317,184],[-9,-4],[
-38,-39],[10,5],[
-39,-26],[60,44],[-6,-2],[
35,26],[-63,-27],[
-82,-40],[62,32],[
33,15],[-4,-1],[
-16,1],[-10,2],[-54,-41],[
-37,-18],[-1,-11],[
41,12],[43,6],[
13,-7],[-89,-54],[-109,-61],[
28,18],[-116,-52],[
10,9],[-166,-92],[
87,41],[-107,-61],[
-94,-60],[-179,-112],[
-272,-161],[117,73],[
65,38],[32,16],[
-30,-23],[27,7],[-257,-142],
[-27,-19],[-41,-12],[
107,71],[21,29],[
-4,7],[-250,-143],[-289,-169
],[6,6],[70,40],[
-14,-5],[57,33],[
-84,-49],[6,5],[-43,-25],[
74,42],[101,61],[
-78,-44],[-37,-24],[3,0],[
6,7],[5,2],[
88,48],[43,25],[12,9],[
-43,-25],[-35,-20],[
2,-2],[122,69],[
143,82],[-23,-11],[9,14],[
-2,2],[49,31],[
14,2],[47,28],[80,43],[
59,29],[86,48],[
-26,-11],[-14,-9],[-17,-12],
[13,5],[-5,-8],[
80,49],[-7,-6],[4,10],[
-42,-19],[-9,5],[
-7,0],[60,35],[73,40],[
1,1],[-106,-60],[
16,10],[-117,-67],[116,66],
[-49,-28],[10,5],[
-141,-82],[-203,-117],[
119,69],[61,35],[
8,4],[-22,-13],[5,2],[
-177,-102],[-53,-31],[
-25,-13],[82,48],[
46,28],[1,1],[
-211,-122],[-247,-143],[-16,-8
],[-75,-42],[13,9],[
-55,-31],[100,56],[
-1,0],[66,38],[
-71,-42],[-100,-57],[80,47],[
40,22],[-8,-5],[
-10,-5],[-3,-3],[-79,-46],[
-51,-30],[-14,-6],[
38,23],[37,23],[
-1,-1],[-124,-72],[-146,-85]
],
[[-11,-8],[-126,-6],[
9,8],[-66,-23],[
124,35],[-1,-4],[80,21],[
-40,-58],[-69,-70],[
59,53],[27,27],[
-1,-5],[25,-22],[22,-21],[
-111,-26],[-33,-33],[
-50,14],[0,43],[
-27,58],[-44,26],[-126,-63],
[-131,-84],[29,19],[
-112,-80],[15,11],[
-191,-114],[95,63],[
-126,-71],[-114,-58],[
-231,-125],[-336,-186],[
152,83],[80,43],[
29,18],[-53,-19],[20,18],[
-292,-177],[-41,-22],[
-27,-24],[144,73],[
60,17],[14,-5],[
-300,-176],[-352,-203],[-7,-5
],[-15,-18],[7,2],[
-13,-10],[31,24],[
2,1],[28,19],[
-25,-10],[-30,-14],[27,13],[
12,6],[-7,-3],[
-7,0],[-5,2],[-17,-14],[
-21,-10],[4,-5],[
14,2],[22,2],[3,-4],[
-38,-23],[-47,-25],[
-44,-25],[412,229],[
-59,-34],[517,296],[
-396,-225],[267,154],[
111,70],[605,355],[
881,513],[-463,-271],[
-241,-140],[-58,-33],[
102,63],[-46,-21],[
792,452],[175,103],[
106,56],[-359,-213],[
-158,-100],[-1,-8],[
870,502],[1019,588],[
4,6],[-47,-9],[
-1,4],[-46,-21],[35,8],[
-23,-12],[-13,-15],[
-39,-33],[-68,-43],[
29,25],[22,12],[
12,4],[-2,-7],[11,-5],[
-70,-34],[-7,-9],[
-24,2],[22,24],[
-6,17],[-5,6],[-67,-38],[
-76,-47],[11,5],[
-55,-37],[11,4],[-83,-49],[
51,33],[-48,-29],[
-34,-18],[-101,-55],[
-144,-82],[71,39],[
35,21],[9,7],[
-19,-10],[7,7],[-127,-75],[
-24,-13],[-11,-11],[
61,32],[28,10],[
3,-1],[-136,-79],[-160,-91],
[-9,-6],[21,-14],[
5,0],[16,3],[
2,16],[14,8],[25,25],[
-3,13],[8,15],[
8,-4],[0,-3],[-12,-4],[
-9,7],[-14,6],[
30,4],[-13,-2],[19,-7],[
5,-14],[29,-12],[
14,-11],[8,2],[4,6],[
-11,-6],[-145,-96],[
27,15],[-148,-88],[
179,110],[-45,-25],[
58,38],[-192,-105],[
-270,-150],[177,99],[
89,49],[-1,0],[
-34,-13],[-4,4],[-219,-134],[
-93,-51],[-25,-22],[
114,58],[86,36],[
8,-5],[-291,-170],[-346,-198
],[10,8],[-129,-45],[
11,11],[-140,-73],[
116,49],[-70,-40],[
-22,-24],[-143,-99],[
-220,-137],[111,74],[
59,37],[18,7],[
-16,-22],[25,-2],[-216,-111],
[-38,-29],[-45,-4],[
78,64],[14,41],[
-15,11],[-226,-128],[-258,
-154],[8,5],[-69,-53],[
12,6],[-97,-59],[
72,49],[-50,-28],[-23,-9],[
-124,-65],[-177,-96],[
95,52],[51,27],[
11,7],[-26,-8],[1,7],[
-146,-92],[-38,-19],[
-13,-16],[79,37],[
46,12],[11,-4],[
-168,-99],[-201,-114],[13,5
],[96,53],[-15,-11],[
86,48],[-120,-67],[
21,10],[-56,-30],[
105,63],[151,86],[
-102,-62],[-53,-28],[
3,3],[17,8],[
-2,2],[125,73],[57,34],[
21,8],[-59,-35],[
-44,-28],[0,1],[171,100],[
202,117],[-4,0],[
-100,-40],[12,10],[-95,-50],
[106,51],[-36,-20],[
25,6],[-102,-69],[
-153,-94],[89,59],[
47,28],[3,0],[
-14,-14],[15,-3],[-144,-75],[
-42,-29],[-29,-3],[
54,42],[22,32],[
-10,5],[-169,-97],[-195,-115
],[3,3],[-29,-39],[
6,4],[-53,-36],[
39,34],[-29,-15],[-15,1],[
-79,-34],[-109,-52],[
61,29],[33,15],[
6,4],[-22,0],[-8,7],[
-77,-58],[-26,-10],[
-1,-14],[54,17],[
42,0],[17,-8],[-97,-59],[
-119,-67],[-2,0],[
-1,10],[-4,0],[
10,9],[-3,-8],[7,5],[
9,0],[21,5],[
24,11],[-14,-3],[-4,-2],[
1,-1],[7,0],[
2,-5],[15,13],[6,1],[
-6,5],[-14,-1],[
-12,4],[-5,4],[20,12],[
25,13],[36,20],[
-50,-8],[-2,0],[-95,-50],[
2,-11],[-81,-48],[
-121,-77],[-88,-62],[
-142,-91],[38,27],[
24,18],[34,18],[
-9,-17],[24,4],[-155,-78],[
16,5],[-30,-4],[
54,45],[-18,13],[-8,12],[
-113,-62],[-126,-76],[
14,10],[12,22],[
-9,-2],[0,3],[-39,-32],[
-19,-11],[-58,-37],[
15,2],[13,2],[
-29,-13],[-12,-5],[13,6],[
4,-3],[13,-1],[
-6,4],[29,13],[-9,6],[
-9,4],[-32,-1],[
-6,6],[28,18],[38,18],[
5,4],[-14,-3],[
-1,1],[-22,-11],[6,0],[
-17,-9],[-20,-14],[
-20,-15],[-33,-20],[
10,8],[8,4],[
7,3],[-3,-3],[5,0],[
-33,-18],[0,-1],[
-8,0],[11,10],[-3,4],[
-1,2],[-28,-16],[
-32,-19],[21,11],[-7,-15],[
3,-1],[-52,-33],[
-11,0],[-51,-30],[-81,-42],
[-64,-30],[-92,-50],[
26,11],[13,7],[
15,10],[-17,-6],[8,11],[
-82,-52],[6,6],[
-1,-9],[44,18],[10,-6],[
8,-3],[-65,-38],[
-77,-43],[18,12],[-75,-42],
[8,6],[-117,-66],[
60,33],[-76,-43],[
-65,-40],[-132,-78],[
-197,-112],[85,52],[
48,26],[21,11],[
-25,-14],[15,7],[-177,-104],
[-22,-13],[-24,-11],[
80,47],[25,16],[
4,1],[-178,-104],[-208,-120
],[-10,-5],[-33,-2],[
2,3],[-6,1],[
38,12],[13,8],[44,18],[
2,-9],[-2,-7],[
13,14],[8,6],[-3,-4],[
9,-3],[2,-8],[
-8,3],[-15,-12],[-13,5],[
-7,7],[-5,16],[
-10,6],[-22,-11],[-23,-15],[
11,9],[112,74],[
-24,-11],[109,65],[-145,-90
],[27,17],[-62,-39],[
144,78],[198,112],[
-138,-75],[-64,-38],[
7,2],[22,11],[
6,-3],[162,97],[75,41],[
15,17],[-82,-42],[
-69,-29],[-2,3],[
223,129],[264,150],[-17,-13
],[-62,-63],[21,7],[
-55,-39],[104,77],[
2,0],[75,54],[
-95,-40],[-119,-60],[102,49],
[46,25],[-15,-5],[
-20,-1],[-19,5],[
-78,-57],[-67,-32],[5,-18],
[57,16],[72,11],[
12,-10],[-142,-84],[
-173,-95]]>;

return _LR;
