//Standard generators of L3(7) are a, b where a has order 2, b has order 3,
//ab has order 19 and ababb has order 6.
//Standard generators of 3.L3(7) are preimages A, B where A has order 2 and AB
//has order 19. 
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI:=[ [a,b^-1], //duality
               [a, a*b*a*b*a*b^-1*a*b^-1*a*b^-1*a*b*(a*b*a*b*a*b*a*b^2)^19] ]
              where a is (_LR`F).1 where b is (_LR`F).2;
//two constituents
_LR`G :=
/*
Original group: c9Group("3l37p")
Direct induction from degree 2
Schur index: 1
Character: ( 114, -14, -57, -57, 0, 2, 7, 7, -2, 4, -2, 16, 2, 2, 2, 2, 2, -1, 
-1, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -8, -8, -1, -1, -1, -1, -1, -1, -1, -1,
-1, -1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 )
*/

MatrixGroup<114,IntegerRing() |
Matrix(SparseMatrix(114,114,\[
1,3,1,1,4,1,1,1,1,1,2,1,1,9,1,1,10,1,1,13,1,1,
14,1,1,5,1,1,6,1,1,19,1,1,20,1,1,7,1,1,8,1,1,21,1,
1,22,1,1,23,1,1,24,1,1,11,1,1,12,1,1,15,1,1,16,1,
1,17,1,1,18,1,1,25,-1,1,26,-1,1,31,1,1,32,1,1,36,1,
2,35,-1,36,-1,1,27,1,1,28,1,1,33,-1,1,34,-1,2,29,-1,
30,-1,1,29,1,2,43,-1,44,-1,1,43,1,2,45,-1,46,-1,1,
45,1,2,49,-1,50,-1,1,49,1,1,38,1,2,37,-1,38,-1,1,40,1,
2,39,-1,40,-1,1,57,1,1,58,1,1,42,1,2,41,-1,42,-1,1,
61,-1,1,62,-1,1,63,1,1,64,1,1,55,-1,1,56,-1,1,47,1,
1,48,1,1,59,-1,1,60,-1,1,51,-1,1,52,-1,1,53,1,1,
54,1,1,77,1,1,78,1,1,79,1,1,80,1,1,81,1,1,82,1,1,
71,-1,1,72,-1,1,85,1,1,86,1,1,90,1,2,89,-1,90,-1,1,
65,1,1,66,1,1,67,1,1,68,1,1,69,1,1,70,1,1,97,1,1,
98,1,1,73,1,1,74,1,1,87,1,1,88,1,2,75,-1,76,-1,1,
75,1,2,101,1,102,1,1,101,-1,1,103,1,1,104,1,1,107,1,
1,108,1,1,83,1,1,84,1,1,99,-1,1,100,-1,1,92,-1,2,
91,1,92,1,1,93,1,1,94,1,1,105,-1,1,106,-1,1,95,1,1,
96,1,1,113,1,1,114,1,1,111,-1,1,112,-1,1,109,1,1,110,1
])),Matrix(SparseMatrix(114,114,\[
1,5,1,1,6,1,1,7,1,1,8,1,1,11,1,1,12,1,1,15,1,1,
16,1,1,17,1,1,18,1,1,1,1,1,2,1,2,13,-1,14,-1,1,13,1,
1,3,1,1,4,1,1,25,1,1,26,1,1,20,1,2,19,-1,20,-1,1,
27,1,1,28,1,1,30,1,2,29,-1,30,-1,1,9,1,1,10,1,1,
33,1,1,34,1,1,37,1,1,38,1,1,39,1,1,40,1,1,21,1,1,
22,1,1,41,1,1,42,1,2,23,-1,24,-1,1,23,1,1,47,1,1,
48,1,1,51,1,1,52,1,1,53,1,1,54,1,1,56,-1,2,55,1,
56,1,1,31,1,1,32,1,2,59,-1,60,-1,1,59,1,1,35,1,1,
36,1,1,66,-1,2,65,1,66,1,1,67,-1,1,68,-1,1,69,1,1,
70,1,1,71,1,1,72,1,2,73,1,74,1,1,73,-1,1,75,-1,1,
76,-1,2,43,1,44,1,1,43,-1,2,45,-1,46,-1,1,45,1,1,
83,1,1,84,1,1,50,1,2,49,-1,50,-1,1,87,1,1,88,1,1,
91,-1,1,92,-1,1,93,1,1,94,1,1,95,1,1,96,1,2,97,1,
98,1,1,97,-1,1,57,1,1,58,1,1,79,1,1,80,1,1,62,-1,
2,61,1,62,1,2,99,1,100,1,1,99,-1,1,63,1,1,64,1,1,
105,1,1,106,1,1,85,1,1,86,1,1,102,1,2,101,-1,102,-1,
2,109,1,110,1,1,109,-1,1,81,-1,1,82,-1,2,107,1,108,1,
1,107,-1,1,77,1,1,78,1,1,111,1,1,112,1,2,89,-1,90,-1,
1,89,1,1,104,-1,2,103,1,104,1,1,113,1,1,114,1
]))>;

return _LR;
