//Standard generators of L4(4) are a, b where a is in class 2B,
//b is in class 4A and ab has order 30.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI:=[ [a, b^-1], //duality
     [a,a*b*a*b^2*a*b^-1*a*b^2*a*b*a*b*a*b^-1*a*b*a*b], //galois
     [a,a*b^-1*a*b^2*a*b*a*b^2*a*b^-1*a*b^-1*a*b*a*b^-1*a*b^-1] ]
              where a is (_LR`F).1 where b is (_LR`F).2;
//two constituents
_LR`G :=
/*
Original group: c9Group("l44p")
Direct induction from degree 2
Schur index: 1
Character: ( 170, 42, 10, -19, -19, -10, 8, 10, 2, 0, 0, 10, 10, 0, -6, -6, -3, 
-3, -2, 0, 2, 2, -1, -1, 0, 0, 2, 2, 1, 1, -5, -5, -5, -5, 0, 0, 0, 0, 1, 1, 1, 
1, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 
-1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 )
*/

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

return _LR;
