//Standard generators of L2(31) are a and b where a has order 2, b has order 3
//and ab has order 31.
//Standard generators of the double cover 2.L2(31) = SL2(31) are preimages A and
//B where B has order 3 and AB has order 31.
_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 fixed by auto
_LR`G :=
/*
Original group: c9Group("sl231p")
Direct integral method
Schur index: 2
Character: ( 128, -128, -4, 0, -2, -2, 4, 0, 0, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 
-1, -1, -1, -1, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4 )
*/

MatrixGroup<256,IntegerRing() |
Matrix(SparseMatrix(256,256,\[
1,155,-1,1,156,-1,1,157,-1,1,158,-1,1,159,-1,1,160,-1,
4,153,1,155,1,157,1,159,1,4,154,1,156,1,158,1,160,1,
1,129,1,1,130,1,1,131,1,1,132,1,1,133,1,1,134,1,1,
135,1,1,136,1,1,232,-1,2,231,1,232,1,4,226,1,228,1,
230,1,232,1,8,225,-1,226,-1,227,-1,228,-1,229,-1,230,-1,
231,-1,232,-1,1,226,-1,2,225,1,226,1,1,228,-1,2,227,1,
228,1,1,191,1,1,192,1,4,185,-1,187,-1,189,-1,191,-1,
4,186,-1,188,-1,190,-1,192,-1,1,185,1,1,186,1,1,187,1,
1,188,1,1,91,1,1,92,1,1,93,1,1,94,1,1,95,1,1,96,1,
4,89,-1,91,-1,93,-1,95,-1,4,90,-1,92,-1,94,-1,96,-1,
2,221,1,222,1,1,221,-1,2,223,1,224,1,1,223,-1,8,
217,-1,218,-1,219,-1,220,-1,221,-1,222,-1,223,-1,224,-1,
4,217,1,219,1,221,1,223,1,2,217,1,218,1,1,217,-1,1,
124,1,2,123,-1,124,-1,1,126,1,2,125,-1,126,-1,1,128,1,
2,127,-1,128,-1,4,122,-1,124,-1,126,-1,128,-1,8,121,1,
122,1,123,1,124,1,125,1,126,1,127,1,128,1,1,174,1,2,
173,-1,174,-1,1,176,1,2,175,-1,176,-1,4,170,-1,172,-1,
174,-1,176,-1,8,169,1,170,1,171,1,172,1,173,1,174,1,
175,1,176,1,1,170,1,2,169,-1,170,-1,1,244,1,2,243,-1,
244,-1,1,246,1,2,245,-1,246,-1,1,248,1,2,247,-1,248,-1,
4,242,-1,244,-1,246,-1,248,-1,8,241,1,242,1,243,1,244,1,
245,1,246,1,247,1,248,1,2,115,1,116,1,1,115,-1,2,117,1,
118,1,1,117,-1,2,119,1,120,1,1,119,-1,8,113,-1,114,-1,
115,-1,116,-1,117,-1,118,-1,119,-1,120,-1,4,113,1,115,1,
117,1,119,1,4,162,1,164,1,166,1,168,1,8,161,-1,162,-1,
163,-1,164,-1,165,-1,166,-1,167,-1,168,-1,1,162,-1,2,
161,1,162,1,1,164,-1,2,163,1,164,1,1,166,-1,2,165,1,
166,1,4,33,1,35,1,37,1,39,1,4,34,1,36,1,38,1,40,1,
1,33,-1,1,34,-1,1,35,-1,1,36,-1,1,37,-1,1,38,-1,
2,111,1,112,1,1,111,-1,8,105,-1,106,-1,107,-1,108,-1,
109,-1,110,-1,111,-1,112,-1,4,105,1,107,1,109,1,111,1,
2,105,1,106,1,1,105,-1,2,107,1,108,1,1,107,-1,1,102,1,
2,101,-1,102,-1,1,104,1,2,103,-1,104,-1,4,98,-1,100,-1,
102,-1,104,-1,8,97,1,98,1,99,1,100,1,101,1,102,1,103,1,
104,1,1,98,1,2,97,-1,98,-1,4,74,-1,76,-1,78,-1,80,-1,
8,73,1,74,1,75,1,76,1,77,1,78,1,79,1,80,1,1,74,1,
2,73,-1,74,-1,1,76,1,2,75,-1,76,-1,1,78,1,2,77,-1,
78,-1,8,49,-1,50,-1,51,-1,52,-1,53,-1,54,-1,55,-1,
56,-1,4,49,1,51,1,53,1,55,1,2,49,1,50,1,1,49,-1,2,
51,1,52,1,1,51,-1,2,53,1,54,1,1,53,-1,1,9,-1,1,
10,-1,1,11,-1,1,12,-1,1,13,-1,1,14,-1,1,15,-1,1,
16,-1,1,204,-1,2,203,1,204,1,1,206,-1,2,205,1,206,1,
1,208,-1,2,207,1,208,1,4,202,1,204,1,206,1,208,1,8,
201,-1,202,-1,203,-1,204,-1,205,-1,206,-1,207,-1,208,-1,
2,183,-1,184,-1,1,183,1,8,177,1,178,1,179,1,180,1,
181,1,182,1,183,1,184,1,4,177,-1,179,-1,181,-1,183,-1,2,
177,-1,178,-1,1,177,1,2,179,-1,180,-1,1,179,1,4,1,-1,
3,-1,5,-1,7,-1,4,2,-1,4,-1,6,-1,8,-1,1,1,1,1,2,1,1,
3,1,1,4,1,1,5,1,1,6,1,2,83,-1,84,-1,1,83,1,2,85,-1,
86,-1,1,85,1,2,87,-1,88,-1,1,87,1,8,81,1,82,1,83,1,
84,1,85,1,86,1,87,1,88,1,4,81,-1,83,-1,85,-1,87,-1,
2,63,1,64,1,1,63,-1,8,57,-1,58,-1,59,-1,60,-1,61,-1,
62,-1,63,-1,64,-1,4,57,1,59,1,61,1,63,1,2,57,1,58,1,
1,57,-1,2,59,1,60,1,1,59,-1,1,150,-1,2,149,1,150,1,
1,152,-1,2,151,1,152,1,4,146,1,148,1,150,1,152,1,8,
145,-1,146,-1,147,-1,148,-1,149,-1,150,-1,151,-1,152,-1,
1,146,-1,2,145,1,146,1,1,29,-1,1,30,-1,1,31,-1,1,
32,-1,4,25,1,27,1,29,1,31,1,4,26,1,28,1,30,1,32,1,1,
25,-1,1,26,-1,2,211,-1,212,-1,1,211,1,2,213,-1,214,-1,
1,213,1,2,215,-1,216,-1,1,215,1,8,209,1,210,1,211,1,
212,1,213,1,214,1,215,1,216,1,4,209,-1,211,-1,213,-1,
215,-1,8,137,1,138,1,139,1,140,1,141,1,142,1,143,1,144,1,
4,137,-1,139,-1,141,-1,143,-1,2,137,-1,138,-1,1,137,1,
2,139,-1,140,-1,1,139,1,2,141,-1,142,-1,1,141,1,4,
194,1,196,1,198,1,200,1,8,193,-1,194,-1,195,-1,196,-1,
197,-1,198,-1,199,-1,200,-1,1,194,-1,2,193,1,194,1,1,
196,-1,2,195,1,196,1,1,198,-1,2,197,1,198,1,1,48,1,
2,47,-1,48,-1,4,42,-1,44,-1,46,-1,48,-1,8,41,1,42,1,
43,1,44,1,45,1,46,1,47,1,48,1,1,42,1,2,41,-1,42,-1,
1,44,1,2,43,-1,44,-1,2,21,-1,22,-1,1,21,1,2,23,-1,
24,-1,1,23,1,8,17,1,18,1,19,1,20,1,21,1,22,1,23,1,
24,1,4,17,-1,19,-1,21,-1,23,-1,2,17,-1,18,-1,1,17,1,
4,249,-1,251,-1,253,-1,255,-1,4,250,-1,252,-1,254,-1,
256,-1,1,249,1,1,250,1,1,251,1,1,252,1,1,253,1,1,
254,1,8,65,-1,66,-1,67,-1,68,-1,69,-1,70,-1,71,-1,
72,-1,4,65,1,67,1,69,1,71,1,2,65,1,66,1,1,65,-1,2,
67,1,68,1,1,67,-1,2,69,1,70,1,1,69,-1,1,235,-1,1,
236,-1,1,237,-1,1,238,-1,1,239,-1,1,240,-1,4,233,1,
235,1,237,1,239,1,4,234,1,236,1,238,1,240,1
])),Matrix(SparseMatrix(256,256,\[
1,155,1,1,156,1,1,157,1,1,158,1,1,159,1,1,160,1,
4,153,-1,155,-1,157,-1,159,-1,4,154,-1,156,-1,158,-1,
160,-1,1,101,-1,1,102,-1,1,103,-1,1,104,-1,4,97,1,99,1,
101,1,103,1,4,98,1,100,1,102,1,104,1,1,97,-1,1,98,-1,
1,145,-1,1,146,-1,1,147,-1,1,148,-1,1,149,-1,1,150,-1,
1,151,-1,1,152,-1,1,74,-1,2,73,1,74,1,1,76,-1,2,75,1,
76,1,1,78,-1,2,77,1,78,1,1,80,-1,2,79,1,80,1,4,25,1,
27,1,29,1,31,1,4,26,1,28,1,30,1,32,1,1,25,-1,1,26,-1,
1,27,-1,1,28,-1,1,29,-1,1,30,-1,2,209,-1,210,-1,1,
209,1,2,211,-1,212,-1,1,211,1,2,213,-1,214,-1,1,213,1,
2,215,-1,216,-1,1,215,1,4,249,-1,251,-1,253,-1,255,-1,
4,250,-1,252,-1,254,-1,256,-1,1,249,1,1,250,1,1,251,1,
1,252,1,1,253,1,1,254,1,8,9,1,10,1,11,1,12,1,13,1,
14,1,15,1,16,1,4,9,-1,11,-1,13,-1,15,-1,2,9,-1,10,-1,
1,9,1,2,11,-1,12,-1,1,11,1,2,13,-1,14,-1,1,13,1,1,
47,1,1,48,1,4,41,-1,43,-1,45,-1,47,-1,4,42,-1,44,-1,
46,-1,48,-1,1,41,1,1,42,1,1,43,1,1,44,1,2,35,-1,
36,-1,1,35,1,2,37,-1,38,-1,1,37,1,2,39,-1,40,-1,1,
39,1,8,33,1,34,1,35,1,36,1,37,1,38,1,39,1,40,1,4,
33,-1,35,-1,37,-1,39,-1,1,125,-1,1,126,-1,1,127,-1,1,
128,-1,4,121,1,123,1,125,1,127,1,4,122,1,124,1,126,1,
128,1,1,121,-1,1,122,-1,2,191,1,192,1,1,191,-1,8,
185,-1,186,-1,187,-1,188,-1,189,-1,190,-1,191,-1,192,-1,
4,185,1,187,1,189,1,191,1,2,185,1,186,1,1,185,-1,2,
187,1,188,1,1,187,-1,4,58,1,60,1,62,1,64,1,8,57,-1,
58,-1,59,-1,60,-1,61,-1,62,-1,63,-1,64,-1,1,58,-1,2,
57,1,58,1,1,60,-1,2,59,1,60,1,1,62,-1,2,61,1,62,1,2,
105,-1,106,-1,1,105,1,2,107,-1,108,-1,1,107,1,2,109,-1,
110,-1,1,109,1,2,111,-1,112,-1,1,111,1,2,195,1,196,1,1,
195,-1,2,197,1,198,1,1,197,-1,2,199,1,200,1,1,199,-1,8,
193,-1,194,-1,195,-1,196,-1,197,-1,198,-1,199,-1,200,-1,
4,193,1,195,1,197,1,199,1,1,141,1,1,142,1,1,143,1,
1,144,1,4,137,-1,139,-1,141,-1,143,-1,4,138,-1,140,-1,
142,-1,144,-1,1,137,1,1,138,1,1,51,1,1,52,1,1,53,1,1,
54,1,1,55,1,1,56,1,4,49,-1,51,-1,53,-1,55,-1,4,50,-1,
52,-1,54,-1,56,-1,1,83,-1,1,84,-1,1,85,-1,1,86,-1,1,
87,-1,1,88,-1,4,81,1,83,1,85,1,87,1,4,82,1,84,1,86,1,
88,1,1,245,1,1,246,1,1,247,1,1,248,1,4,241,-1,243,-1,
245,-1,247,-1,4,242,-1,244,-1,246,-1,248,-1,1,241,1,1,
242,1,2,219,1,220,1,1,219,-1,2,221,1,222,1,1,221,-1,
2,223,1,224,1,1,223,-1,8,217,-1,218,-1,219,-1,220,-1,
221,-1,222,-1,223,-1,224,-1,4,217,1,219,1,221,1,223,1,
1,179,-1,1,180,-1,1,181,-1,1,182,-1,1,183,-1,1,184,-1,
4,177,1,179,1,181,1,183,1,4,178,1,180,1,182,1,184,1,2,
161,1,162,1,1,161,-1,2,163,1,164,1,1,163,-1,2,165,1,
166,1,1,165,-1,2,167,1,168,1,1,167,-1,4,170,-1,172,-1,
174,-1,176,-1,8,169,1,170,1,171,1,172,1,173,1,174,1,
175,1,176,1,1,170,1,2,169,-1,170,-1,1,172,1,2,171,-1,
172,-1,1,174,1,2,173,-1,174,-1,1,231,-1,1,232,-1,4,
225,1,227,1,229,1,231,1,4,226,1,228,1,230,1,232,1,1,
225,-1,1,226,-1,1,227,-1,1,228,-1,4,233,-1,235,-1,
237,-1,239,-1,4,234,-1,236,-1,238,-1,240,-1,1,233,1,
1,234,1,1,235,1,1,236,1,1,237,1,1,238,1,1,202,1,2,
201,-1,202,-1,1,204,1,2,203,-1,204,-1,1,206,1,2,205,-1,
206,-1,1,208,1,2,207,-1,208,-1,1,70,1,2,69,-1,70,-1,1,
72,1,2,71,-1,72,-1,4,66,-1,68,-1,70,-1,72,-1,8,65,1,
66,1,67,1,68,1,69,1,70,1,71,1,72,1,1,66,1,2,65,-1,
66,-1,1,8,-1,2,7,1,8,1,4,2,1,4,1,6,1,8,1,8,1,-1,
2,-1,3,-1,4,-1,5,-1,6,-1,7,-1,8,-1,1,2,-1,2,1,1,2,1,
1,4,-1,2,3,1,4,1,4,90,-1,92,-1,94,-1,96,-1,8,89,1,
90,1,91,1,92,1,93,1,94,1,95,1,96,1,1,90,1,2,89,-1,
90,-1,1,92,1,2,91,-1,92,-1,1,94,1,2,93,-1,94,-1,1,
114,-1,2,113,1,114,1,1,116,-1,2,115,1,116,1,1,118,-1,
2,117,1,118,1,1,120,-1,2,119,1,120,1,1,23,-1,1,24,-1,
4,17,1,19,1,21,1,23,1,4,18,1,20,1,22,1,24,1,1,17,-1,
1,18,-1,1,19,-1,1,20,-1,1,129,1,1,130,1,1,131,1,1,
132,1,1,133,1,1,134,1,1,135,1,1,136,1
]))>;

return _LR;
