//L3(9) not on online ATLAS.
//I have taken standard generators of U3(9) as a and b where a has order 2,
//b is in class 3B and ab has order 24.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
   _LR`AI:=[ [a, b^-1], //duality
  [a, (b*a)^6 * (b^-1*a)^6 * b^-1], //galois
  [a, (b^-1*a)^6 * (b*a)^6 * b]]
                  where a is (_LR`F).1 where b is (_LR`F).2;
//2 constituents
_LR`G :=
/*
Original group: c9Group("l39p")
Direct induction from degree 1
Schur index: 1
Character: ( 182, 22, 20, 2, -18, -18, -2, 2, 2, 4, 0, 0, -2, -2, -2, -2, -2, 
-2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, 
-2, -2, -2, -2, -2, -2, -2, -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 )
*/

MatrixGroup<182,IntegerRing() |
Matrix(SparseMatrix(182,182,\[
1,3,1,1,4,1,1,1,1,1,2,1,1,13,1,1,14,-1,1,15,1,
1,16,1,1,17,1,1,18,1,1,19,1,1,20,1,1,5,1,1,6,-1,
1,7,1,1,8,1,1,9,1,1,10,1,1,11,1,1,12,1,1,21,1,1,
22,1,1,31,1,1,32,1,1,33,1,1,34,1,1,35,1,1,36,1,1,
37,1,1,38,1,1,23,1,1,24,1,1,25,1,1,26,1,1,27,1,1,
28,1,1,29,1,1,30,1,1,55,1,1,56,1,1,57,1,1,58,1,1,
59,1,1,60,1,1,61,1,1,62,1,1,47,1,1,48,1,1,63,1,1,
64,-1,1,65,1,1,66,1,1,67,1,1,68,1,1,39,1,1,40,1,
1,41,1,1,42,1,1,43,1,1,44,1,1,45,1,1,46,1,1,49,1,
1,50,-1,1,51,1,1,52,1,1,53,1,1,54,1,1,69,1,1,70,1,
1,117,1,1,118,1,1,121,1,1,122,1,1,123,1,1,124,-1,1,
77,1,1,78,1,1,81,-1,1,82,1,1,79,-1,1,80,1,1,131,-1,
1,132,1,1,125,1,1,126,1,1,141,-1,1,142,-1,1,145,1,1,
146,1,1,129,-1,1,130,1,1,93,1,1,94,1,1,95,1,1,96,1,
1,159,1,1,160,1,1,161,1,1,162,1,1,158,1,1,157,1,
1,167,1,1,168,1,1,116,1,1,115,1,1,134,-1,1,133,1,
1,156,1,1,155,1,1,144,-1,1,143,1,1,113,1,1,114,1,
1,106,1,1,105,1,1,71,1,1,72,1,1,119,1,1,120,1,1,
73,1,1,74,1,1,75,1,1,76,-1,1,85,1,1,86,1,1,135,1,
1,136,1,1,91,-1,1,92,1,1,83,-1,1,84,1,1,108,1,1,
107,-1,1,127,1,1,128,1,1,137,1,1,138,1,1,139,1,1,
140,1,1,87,-1,1,88,-1,1,112,1,1,111,-1,1,89,1,1,
90,1,1,165,-1,1,166,1,1,163,1,1,164,1,1,179,1,1,
180,1,1,176,1,1,175,1,1,110,1,1,109,1,1,102,1,1,
101,1,1,97,1,1,98,1,1,99,1,1,100,1,1,149,1,1,150,1,
1,147,-1,1,148,1,1,103,1,1,104,1,1,177,1,1,178,-1,
1,182,1,1,181,1,1,173,1,1,174,1,1,154,1,1,153,1,1,
169,1,1,170,-1,1,151,1,1,152,1,1,172,1,1,171,1
])),Matrix(SparseMatrix(182,182,\[
1,5,1,1,6,1,1,9,1,1,10,1,1,7,1,1,8,-1,1,1,1,1,2,-1,
1,11,1,1,12,1,1,3,1,1,4,1,1,21,1,1,22,1,1,25,1,1,
26,1,1,16,1,1,15,1,1,27,1,1,28,1,1,23,1,1,24,1,1,
13,1,1,14,1,1,18,1,1,17,1,1,29,1,1,30,1,1,19,1,1,
20,1,1,39,1,1,40,-1,1,43,1,1,44,1,1,47,1,1,48,1,1,
51,1,1,52,1,1,41,1,1,42,1,1,31,1,1,32,-1,1,45,1,1,
46,1,1,33,1,1,34,1,1,49,1,1,50,1,1,35,1,1,36,1,1,
53,1,1,54,1,1,37,1,1,38,1,1,67,1,1,68,1,1,71,1,1,
72,1,1,75,1,1,76,1,1,79,1,1,80,-1,1,111,1,1,112,1,
1,113,1,1,114,1,1,69,1,1,70,-1,1,55,1,1,56,-1,1,
73,1,1,74,1,1,57,1,1,58,1,1,77,1,1,78,1,1,59,1,1,
60,1,1,81,1,1,82,-1,1,61,1,1,62,1,1,133,1,1,134,-1,
1,96,1,1,95,-1,1,143,1,1,144,1,1,147,-1,1,148,1,
1,149,1,1,150,-1,1,153,1,1,154,1,1,140,-1,1,139,1,
1,100,1,1,99,1,1,122,1,1,121,1,1,142,1,1,141,1,1,
119,1,1,120,1,1,66,1,1,65,1,1,137,1,1,138,1,1,91,1,
1,92,-1,1,163,1,1,164,1,1,106,1,1,105,1,1,173,1,1,
174,1,1,93,1,1,94,1,1,162,1,1,161,1,1,97,1,1,98,1,
1,177,1,1,178,1,1,88,-1,1,87,1,1,90,1,1,89,-1,1,
172,1,1,171,1,1,107,1,1,108,1,1,135,1,1,136,1,1,
83,1,1,84,-1,1,131,1,1,132,1,1,85,1,1,86,1,1,166,1,
1,165,1,1,126,1,1,125,-1,1,123,1,1,124,1,1,128,1,
1,127,1,1,109,1,1,110,1,1,176,1,1,175,1,1,117,1,
1,118,1,1,115,1,1,116,1,1,157,1,1,158,1,1,181,1,
1,182,-1,1,104,1,1,103,1,1,63,1,1,64,1,1,101,1,1,
102,1,1,160,-1,1,159,1,1,129,1,1,130,1,1,170,1,1,
169,1,1,155,1,1,156,1,1,179,1,1,180,-1,1,145,1,1,
146,1,1,152,1,1,151,-1,1,168,1,1,167,1
]))>;

return _LR;
