//Standard generators of 2F4(2)' = T are a, b where a is in class 2A,
//b has order 3 and ab has order 13.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI:=[[a,b*a*b*a*b*a*b*a*b^-1*a*b*a*b*a*b*a*b*a*b^-1*a]]
                            where a is (_LR`F).1 where b is (_LR`F).2;
//two constituents fixed by _LR`AI[1]

_LR`G :=
MatrixGroup<27, ext<K|Polynomial(K, [1, 0, 1])> where K is RationalField() |
[[-249,-57],[84,28],[
104,61],[-47,-137],[
92,-64],[-112,100],[
-51,-69],[83,-67],[
56,32],[81,23],[
-121,117],[-78,-56],[-134,85
],[22,-73],[-10,-68],[
32,112],[-84,66],[
-137,16],[9,8],[
50,-117],[70,78],[-1,-73],[
-77,-41],[-9,-86],[
-46,-133],[85,24],[
-89,-54],[-69,-27],[
21,12],[26,23],[
-6,-42],[30,-14],[-37,24],[
-12,-22],[27,-15],[
15,12],[23,10],[
-41,29],[-20,-20],[-42,19],
[11,-21],[0,-20],[
4,34],[-27,15],[
-41,-2],[2,3],[20,-31],[
16,26],[2,-22],[
-20,-15],[2,-25],[-6,-40],[
23,9],[-24,-20],[
-21,-25],[6,9],[6,14],[
6,-17],[14,1],[
-20,1],[0,-12],[13,-1],[
3,8],[6,9],[
-22,2],[-4,-12],[-19,-1],[
8,-5],[3,-8],[
-4,14],[-12,1],[-16,-9],[
0,1],[14,-8],[
2,13],[5,-8],[-5,-10],[
6,-9],[6,-16],[
6,9],[-6,-13],[48,67],[
-13,-24],[-14,-35],[
-19,42],[-36,-5],[
49,1],[-3,29],[
-35,-1],[-7,-22],[-13,-23],[
55,-2],[7,30],[
51,10],[-20,12],[-11,19],[
16,-33],[33,1],[
37,23],[1,-2],[-38,17],[
-2,-34],[-15,17],[
10,26],[-16,23],[
-16,42],[-14,-24],[11,33],[
-10,-122],[0,40],[
-13,51],[57,-39],[
43,34],[-63,-38],[
24,-35],[41,28],[
-3,32],[0,42],[-72,-40],[
15,-43],[-60,-53],[
35,3],[30,-14],[
-47,28],[-40,-29],[-23,-58],
[-6,4],[61,6],[
-25,42],[35,-10],[8,-39],[
35,-16],[52,-39],[
2,44],[12,-48],[
62,-75],[-25,21],[-38,20],[
57,10],[6,44],[
-16,-57],[32,-7],[8,40],[
-19,17],[-23,25],[
-21,-63],[33,-17],[
-6,-64],[21,23],[
24,8],[-44,-11],[-6,-40],[
19,-47],[-7,0],[
32,38],[-39,10],[26,13],[
27,-18],[30,12],[
52,8],[-22,26],[33,-22],[
116,96],[-33,-36],[
-34,-56],[-16,85],[
-68,8],[88,-22],[
9,52],[-62,13],[-26,-33],[
-37,-36],[98,-30],[
26,51],[98,-7],[
-33,30],[-13,39],[16,-67],[
61,-12],[73,27],[
1,-8],[-59,49],[-16,-60],[
-20,39],[28,41],[
-17,47],[-11,80],[-39,-35],
[34,53],[-37,-85],[
7,30],[0,41],[
34,-44],[40,15],[-55,-12],[
8,-30],[37,11],[
5,24],[12,30],[-63,-10],[
0,-36],[-56,-22],[
29,-8],[18,-18],[
-29,33],[-38,-11],[-33,-37],
[-2,6],[46,-11],[
-10,38],[22,-17],[
-4,-31],[24,-21],[
30,-41],[13,29],[
-4,-39],[325,1],[-106,-16],
[-134,-51],[92,164],[
-101,106],[115,-159],[
86,70],[-86,104],[
-84,-19],[-112,-7],[
121,-185],[113,49],[
150,-146],[-15,100],[
31,80],[-65,-133],[
88,-101],[163,-53],[
-13,-14],[-30,161],[
-107,-79],[22,94],[
104,30],[33,103],[
90,151],[-114,-2],[
128,41],[-121,44],[
41,-10],[57,1],[
-56,-47],[22,-52],[-21,74],
[-41,-14],[18,-50],[
31,-3],[42,-13],[
-21,84],[-49,-4],[-33,76],[
-7,-39],[-23,-26],[
43,41],[-19,50],[
-57,41],[8,3],[-11,-63],[
50,15],[-22,-33],[
-43,3],[-25,-34],[
-53,-43],[43,-16],[
-53,0],[255,62],[
-81,-32],[-100,-66],[43,144
],[-98,64],[119,-102],[
53,71],[-88,66],[
-58,-32],[-85,-25],[128,-121
],[79,60],[143,-88],[
-29,76],[10,70],[
-27,-117],[88,-65],[142,-11
],[-8,-11],[-54,119],[
-70,-82],[1,78],[
77,44],[5,87],[43,136],[
-87,-22],[92,58],[
141,-8],[-46,-5],[
-57,-21],[44,71],[
-41,49],[46,-73],[
40,27],[-34,47],[
-36,-3],[-51,0],[48,-84],[
50,19],[61,-70],[
-6,44],[15,34],[-31,-58],[
37,-46],[70,-24],[
-8,-8],[-7,71],[
-47,-32],[12,42],[46,11],[
16,43],[41,62],[
-52,3],[56,14],[-44,-4],[
13,3],[16,6],[
-8,-23],[16,-12],[-19,19],[
-11,-11],[13,-13],[
13,4],[15,3],[
-20,23],[-14,-9],[-24,18],[
3,-12],[-3,-11],[
5,18],[-13,12],[-22,5],[
-1,3],[7,-22],[
13,11],[-2,-13],[-13,-5],[
-3,-14],[-11,-20],[
15,2],[-17,-8],[
0,0],[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],[0,0],[0,0],[
0,0],[0,0],[0,
0],[0,0],[11,-18],[
-4,6],[-9,5],[
12,-1],[3,8],[-5,-11],[
6,-3],[3,8],[
-1,2],[-4,7],[-5,-12],[
7,-4],[-7,-14],[
4,5],[6,1],[-11,-1],[
-4,-9],[7,-11],[
-2,2],[8,5],[-8,3],[
8,3],[6,-5],[
5,2],[10,0],[-3,8],[
7,-4],[-33,18],[
15,-5],[17,-2],[-21,-11],[
3,-17],[-1,23],[
-12,-1],[2,-15],[8,-4],[
12,-6],[0,25],[
-14,2],[-6,23],[-5,-11],[
-6,-6],[14,10],[
-5,15],[-13,14],[4,1],[
-7,-18],[14,2],[
-6,-8],[-13,3],[-10,-9],[
-18,-11],[14,-6],[
-13,4],[215,39],[
-69,-21],[-87,-49],[42,116],
[-78,57],[94,-90],[
47,57],[-69,59],[
-50,-25],[-72,-17],[102,-106
],[69,46],[113,-79],[
-20,64],[11,57],[
-29,-95],[69,-58],[118,-17],
[-7,-8],[-39,101],[
-62,-64],[5,65],[
66,32],[9,72],[42,110],[
-74,-14],[79,44],[
-220,-16],[69,16],[
88,39],[-52,-115],[
74,-66],[-87,101],[
-55,-53],[63,-67],[
57,18],[75,11],[
-92,119],[-74,-39],[-109,92
],[15,-66],[-18,-56],[
37,93],[-63,65],[
-113,29],[6,10],[29,-108],[
69,58],[-11,-65],[
-69,-25],[-17,-71],[
-54,-105],[76,7],[
-86,-35],[192,-32],[
-66,1],[-85,-16],[
72,88],[-48,73],[
51,-105],[58,31],[-40,70],[
-50,-1],[-67,8],[
52,-121],[71,18],[73,-103],
[2,60],[26,44],[
-51,-72],[43,-68],[92,-46],
[-10,-8],[-1,98],[
-70,-35],[22,53],[
65,8],[29,57],[
69,80],[-69,10],[78,11],[
-99,-14],[31,10],[
41,21],[-20,-54],[
36,-28],[-42,43],[
-23,-27],[31,-29],[
27,12],[33,7],[
-45,52],[-33,-19],[-52,36],[
7,-31],[-6,-26],[
16,43],[-30,28],[-51,13],[
2,3],[17,-48],[
31,29],[-4,-28],[-30,-13],[
-7,-34],[-21,-51],[
32,6],[-39,-18],[
-13,32],[5,-10],[10,-13],[
-19,3],[-6,-14],[
10,17],[-11,5],[-7,-13],[
7,-8],[5,-10],[
13,19],[-9,9],[7,21],[
-10,-4],[-9,0],[
15,-2],[7,12],[0,18],[
0,0],[-14,-10],[
12,-9],[-10,-1],[-6,9],[
-12,0],[-19,4],[
4,-10],[-9,11],[108,-15],[
-35,0],[-48,-8],[
37,50],[-29,40],[31,-58],[
32,21],[-23,39],[
-31,-4],[-37,2],[32,-67],[
40,10],[44,-53],[
1,33],[14,25],[-28,-40],[
23,-38],[49,-28],[
-3,-3],[-3,55],[
-40,-21],[11,29],[36,4],[
17,33],[38,46],[
-38,3],[45,7],[-22,20],[
7,-5],[12,-6],[
-15,-6],[1,-13],[1,18],[
-11,0],[-1,-12],[
9,-3],[8,-6],[2,21],[
-11,4],[-1,17],[
-5,-8],[-8,-2],[13,3],[
2,10],[-7,15],[
0,0],[-7,-13],[13,-2],[
-8,-4],[-9,5],[
-9,-5],[-15,-5],[7,-6],[
-13,6],[20,23],[
-5,-8],[-4,-14],[-6,16],[
-14,-1],[18,-2],[
0,10],[-13,0],[-3,-8],[
-7,-8],[21,-3],[
4,11],[19,2],[-9,6],[
-4,7],[5,-13],[
13,0],[15,8],[-1,-1],[
-13,7],[-1,-13],[
-5,8],[4,9],[-6,9],[
-6,16],[-7,-7],[
5,12],[66,8],[-23,-4],[
-26,-13],[16,34],[
-22,19],[26,-29],[
14,16],[-20,19],[
-15,-6],[-22,-4],[28,-33],[
21,13],[34,-26],[
-4,19],[3,17],[-9,-29],[
22,-19],[34,-6],[
-3,-3],[-9,32],[-19,-19],[
1,20],[21,8],[
5,22],[16,32],[-25,-3],[
23,12],[-15,-41],[
4,15],[1,17],[
16,-20],[18,7],[-25,-7],[
4,-15],[16,5],[
5,11],[4,15],[-28,-6],[
1,-15],[-27,-14],[
11,-2],[9,-7],[
-13,13],[-16,-7],[-10,-16],[
-3,2],[22,-5],[
-4,16],[12,-5],[-1,-14],[
9,-9],[13,-19],[
5,17],[-1,-16],[129,102],[
-36,-39],[-39,-60],[
-16,93],[-73,10],[
96,-27],[13,57],[
-66,15],[-29,-36],[-41,-39],
[107,-36],[30,54],[
105,-8],[-37,34],[
-11,41],[14,-71],[
64,-12],[80,27],[
1,-8],[-63,55],[-19,-64],[
-21,43],[32,44],[
-18,51],[-11,88],[-44,-38],
[40,56]],
[[-55,18],[23,-3],[
29,0],[-30,-22],[
9,-25],[-8,33],[-17,-4],[
10,-22],[12,-3],[
18,-7],[-6,37],[-21,-2],[
-17,33],[-7,-19],[
-9,-11],[19,18],[
-11,22],[-25,18],[5,1],[
-5,-29],[23,6],[
-8,-13],[-22,2],[-11,-15],[
-27,-22],[20,-5],[
-21,2],[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],[-1,0],[0,0],[
0,0],[0,0],[0,
0],[2,-69],[-3,22],[
-9,28],[34,-17],[
21,22],[-32,-26],[16,-17],[
22,19],[-6,18],[
-3,23],[-37,-27],[12,-23],[
-30,-33],[20,3],[
17,-6],[-28,12],[-21,-19],[
-11,-35],[-3,1],[
34,8],[-16,22],[20,-4],[
6,-22],[22,-6],[
31,-19],[-2,24],[10,-27],[
-8,-9],[1,4],[
2,6],[3,-8],[6,0],[
-8,1],[0,-5],[
5,-1],[2,3],[3,3],[
-9,1],[-2,-5],[
-7,1],[3,-2],[1,-4],[
-1,7],[-4,2],[
-6,-3],[0,1],[5,-3],[
1,6],[1,-3],[
-2,-4],[2,-4],[3,-6],[
2,3],[-3,-5],[
-116,103],[42,-28],[65,-26],[
-84,-29],[3,-70],[
9,93],[-54,1],[
-3,-65],[39,-19],[42,-32],[
15,105],[-56,19],[
-8,98],[-28,-40],[
-37,-18],[67,25],[
3,63],[-39,73],[
7,0],[-40,-67],[64,-7],[
-38,-25],[-46,23],[
-46,-25],[-80,-25],[
40,-34],[-60,27],[
14,-12],[-5,2],[
-6,2],[10,6],[-1,9],[
-1,-12],[7,-1],[
0,7],[-5,4],[-6,4],[
-2,-14],[7,-2],[
2,-12],[2,6],[4,2],[
-7,-4],[1,-7],[
4,-8],[-2,-2],[5,9],[
-7,0],[4,3],[
6,-2],[5,3],[9,4],[
-6,4],[7,-4],[
-108,-33],[33,16],[39,31],[
-14,-64],[44,-25],[
-54,41],[-22,-31],[
39,-25],[25,14],[
37,13],[-59,49],[-32,-28],[
-65,35],[16,-32],[
-3,-30],[8,51],[
-39,25],[-60,-1],[3,6],[
26,-50],[28,37],[
2,-35],[-32,-21],[0,-37],[
-15,-59],[38,11],[
-38,-27],[3,35],[
2,-11],[5,-16],[-18,12],[
-13,-10],[18,11],[
-7,10],[-12,-9],[
1,-10],[-1,-12],[22,11],[
-4,13],[18,15],[
-12,0],[-8,5],[14,-9],[
12,8],[7,17],[
1,-2],[-18,-2],[8,-14],[
-10,4],[-3,12],[
-11,5],[-16,12],[-1,-11],[
-3,15],[-3,-74],[
-3,24],[-10,32],[36,-22],[
25,22],[-37,-25],[
15,-19],[25,19],[
-4,18],[0,25],[-43,-26],[
11,-26],[-36,-31],[
23,2],[18,-8],[
-30,16],[-24,-19],[-14,-39],[
-3,3],[37,6],[
-17,25],[21,-7],[6,-25],[
24,-8],[33,-22],[
0,25],[9,-30],[-143,-17],[
46,12],[57,27],[
-32,-76],[49,-41],[-59,63],
[-34,-36],[43,-42],[
36,13],[48,9],[
-63,74],[-47,-28],[-73,57],[
11,-42],[-10,-37],[
22,61],[-43,40],[
-75,15],[4,7],[22,-70],[
44,39],[-5,-42],[
-45,-18],[-9,-47],[-33,-70],
[50,8],[-54,-25],[
-126,183],[48,-53],[
79,-56],[-126,-13],[
-20,-97],[44,126],[
-73,21],[-26,-89],[
44,-39],[48,-60],[
55,140],[-72,44],[
26,142],[-49,-47],[
-58,-14],[101,16],[
25,89],[-34,113],[
13,-1],[-79,-79],[
85,-29],[-63,-24],[
-57,47],[-70,-22],[
-118,-7],[45,-64],[
-74,55],[-20,134],[
11,-44],[26,-53],[
-71,29],[-37,-47],[
57,57],[-36,31],[
-38,-41],[14,-34],[10,-44],
[67,61],[-27,43],[
50,71],[-38,-11],[
-35,9],[57,-20],[
37,40],[12,69],[5,-3],[
-64,-22],[38,-41],[
-40,2],[-17,41],[
-43,9],[-66,30],[8,-47],[
-25,50],[52,50],[
-15,-18],[-15,-30],[-10,40],
[-32,1],[42,-7],[
2,24],[-30,3],[
-8,-18],[-17,-17],[48,-10],[
11,26],[44,-1],[
-18,15],[-7,19],[9,-33],[
30,-5],[37,16],[
-2,-3],[-29,20],[-5,-31],[
-10,19],[13,21],[
-11,23],[-9,39],[-18,-16],[
14,28],[121,114],[
-34,-41],[-33,-66],[
-23,92],[-74,4],[
98,-18],[7,57],[-68,9],[
-24,-37],[-39,-42],[
110,-25],[25,58],[
107,-3],[-41,31],[
-16,42],[21,-73],[
67,-9],[79,38],[
0,-9],[-67,49],[-13,-67],[
-25,44],[28,48],[
-23,49],[-19,87],[-42,-40],
[33,61],[117,267],[
-26,-92],[-8,-131],[
-100,134],[-123,-44],[
171,38],[-27,95],[
-117,-33],[-13,-75],[
-35,-93],[194,33],[
0,110],[175,68],[
-87,25],[-54,56],[85,-103],
[115,33],[103,117],[
6,-14],[-142,33],[
25,-118],[-69,54],[
14,97],[-72,64],[
-90,129],[-39,-92],[12,121],
[-163,37],[55,-3],[
72,9],[-65,-73],[
39,-65],[-40,93],[-51,-26],
[31,-63],[44,0],[
57,-9],[-40,106],[
-63,-13],[-58,92],[
-4,-51],[-25,-37],[
48,61],[-32,62],[
-76,46],[9,7],[-4,-85],[
62,27],[-22,-44],[
-56,-3],[-28,-48],[
-62,-64],[58,-11],[
-69,-6],[-28,48],[
11,-16],[21,-16],[
-32,1],[-8,-23],[
14,30],[-17,6],[-8,-22],[
9,-9],[10,-16],[
16,32],[-17,12],[11,35],[
-14,-10],[-15,-3],[
27,2],[9,23],[
-8,29],[3,-2],[-21,-17],[
22,-9],[-17,-5],[
-13,13],[-18,-4],[-30,1],[
9,-17],[-17,14],[
61,29],[-19,-12],[-23,-22],
[4,39],[-28,11],[
35,-19],[9,21],[
-26,12],[-13,-12],[-20,-10],
[39,-23],[17,20],[
40,-15],[-10,18],[
-1,19],[-2,-32],[
25,-13],[37,4],[-2,-3],[
-20,27],[-14,-25],[
-3,19],[17,15],[
-3,23],[4,37],[-20,-10],[
20,20],[-15,-35],[
1,9],[0,18],[
16,-15],[16,8],[-23,-6],[
4,-13],[15,5],[
1,12],[5,13],[-28,-6],[
0,-15],[-21,-9],[
14,-3],[7,-8],[-11,13],[
-14,-4],[-16,-16],[
-1,1],[19,-2],[
-4,16],[8,-9],[-1,-13],[
11,-8],[14,-16],[
5,10],[-2,-18],[-85,111],[
32,-32],[52,-31],[
-79,-13],[-9,-62],[
24,81],[-46,11],[
-13,-56],[29,-23],[32,-37],
[31,91],[-47,26],[
12,88],[-29,-33],[
-36,-11],[63,13],[
12,57],[-25,71],[
9,-1],[-47,-52],[55,-14],[
-39,-17],[-38,28],[
-44,-16],[-74,-10],[
30,-40],[-49,33],[
108,75],[-32,-28],[
-34,-47],[-7,74],[
-57,11],[74,-25],[
11,43],[-53,15],[
-21,-27],[-35,-28],[83,-32],
[26,43],[82,-15],[
-28,29],[-8,35],[
9,-60],[53,-15],[69,20],[
-2,-7],[-47,46],[
-17,-51],[-14,37],[28,34],[
-13,42],[-4,70],[
-38,-26],[32,45],[-40,-151],
[7,51],[-2,68],[
63,-62],[61,33],[-87,-34],[
22,-50],[59,26],[
2,42],[9,52],[-100,-34],[
9,-58],[-86,-52],[
45,-5],[33,-25],[
-51,46],[-56,-27],[-45,-68],
[-6,6],[79,-6],[
-20,58],[40,-20],[1,-52],[
42,-28],[57,-61],[
11,55],[3,-64],[
-242,36],[80,-1],[104,22],[
-86,-111],[63,-89],[
-68,131],[-71,-42],[
52,-87],[63,4],[
84,-7],[-70,150],[-89,-25],
[-95,127],[1,-75],[
-32,-56],[62,92],[
-54,85],[-117,56],[
11,10],[4,-123],[
88,46],[-27,-69],[-81,-10],
[-35,-72],[-84,-100],[
86,-12],[-99,-17],[
-111,0],[36,5],[
46,16],[-32,-55],[34,-36],[
-39,54],[-29,-24],[
29,-36],[28,6],[
38,3],[-41,62],[-38,-17],[
-52,51],[5,-33],[
-11,-27],[22,45],[-29,35],[
-55,17],[4,5],[
10,-55],[37,26],[-7,-33],[
-36,-10],[-11,-34],[
-32,-50],[39,1],[
-43,-14],[17,-103],[-11,33],
[-22,40],[58,-21],[
29,37],[-45,-45],[
25,-24],[28,33],[
-8,26],[-8,35],[-52,-47],[
22,-32],[-40,-56],[
31,9],[26,-6],[
-45,13],[-26,-33],[-6,-54],[
-7,2],[50,18],[
-29,30],[31,-2],[15,-32],[
33,-5],[52,-22],[
-8,36],[18,-38],[-82,142],[
34,-42],[55,-44],[
-96,-2],[-21,-71],[
41,91],[-52,22],[
-24,-63],[28,-33],[32,-48],
[51,100],[-50,37],[
27,103],[-39,-33],[
-43,-6],[75,6],[
22,64],[-18,84],[11,-2],[
-64,-53],[61,-26],[
-47,-15],[-40,38],[
-53,-11],[-88,1],[
30,-51],[-50,46],[
-14,-155],[-3,54],[
-17,67],[73,-54],[
56,41],[-81,-47],[
28,-45],[54,35],[
-2,39],[2,53],[-92,-48],[
18,-55],[-79,-64],[
46,2],[36,-19],[
-59,38],[-51,-36],[-29,-75],
[-7,7],[78,6],[
-31,55],[44,-13],[10,-52],[
46,-20],[67,-51],[
2,56],[13,-61]]>;

return _LR;
