_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;
//Standard generators of S4(5) are a and b where a is in class 2B, b is in class
//3B and ab is in class 13C. The last condition is equivalent to: ab has order
//13 and ababb has order 12.
//Standard generators of 2.S4(5) are preimages A and B where B has order 3 and
//AB has order 13.

//two constituents interchanged by _LR`[1]
_LR`G :=
/*
Original group: c9Group("s45p")
Direct induction from degree 1
Schur index: 1
Character: ( 156, 12, -12, 0, 6, 4, 0, 31, 31, 6, 6, 1, 1, 6, 0, 0, 7, 7, 2, 2, 
2, -2, 0, -2, 0, 0, 0, 1, 1, 0, -1, -1, 1, 1 )
*/

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

return _LR;
