//Standard generators of L2(16) are a and b where a has order 2, b has order 3
//and ab has order 15.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [a, b^-1*a*b^-1*a*b*a*b^-1*a*b*a],
            [a, b^-1*a*b^-1*a*b^-1*a*b*a*b*a*b^-1*a*b*a*b*a*b]]
                  where a is (_LR`F).1 where b is (_LR`F).2;
//second automorphism is square of first - must handle that somehow!
//four constituents permuted in 4-cycle by _LR`AI[1]
_LR`G := sub<GL(68,Integers()) |
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1,0,0,
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0,1,0,-1,0,1,0,1,0,0,1,0,0,0,0,0,-1,0,-1,-1,1,1,1,-1,1,1,-1,0,0,
1,1,0,1,0,0,0,0,0,0,0,
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0,0,1,
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0,0,0,0,0,0,1,-1,0,0,0,0,0,1,0,1,0,0,0,0,1,-1,0,-1,0,1,-1,0,1,-1,
0,0,-1,0,0,0,0,
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0,0,0,
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-12,1,7,0,0,9,-7,7,31,-4,5,11,-3,-2,27,-10,10,-10,12,11,4,9,-9,-6,
-3,8,4,0,1,-8,-19,-6,-7,-12,6,11,-2,-16,20,7,8,3,-14,
-1,-1,-1,1,0,1,0,-1,0,-4,-6,-1,2,0,-1,0,0,1,1,2,-1,2,-2,-2,0,2,0,
-1,0,1,-2,1,-1,-5,1,1,-1,0,2,-4,2,-2,2,-1,-3,-1,-2,-1,1,1,-1,-1,
2,0,0,3,2,2,2,0,-1,0,2,-3,-2,-2,-1,2,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,
0,0,0,
0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,-1,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,
0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,-1,
1,0,0,0,0,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
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,
0,0,0,
0,0,-1,-1,0,1,0,0,-1,0,2,-1,0,1,0,0,-1,-1,-1,-1,-1,-1,1,1,0,0,1,0,
-1,-1,0,0,-1,1,-1,0,1,0,-1,1,1,1,1,-1,1,0,0,-1,1,1,0,0,-1,0,0,-1,
0,0,0,-1,1,1,-1,0,1,0,0,0,
0,0,0,-1,0,-1,0,0,-1,1,1,1,0,-1,-1,1,0,0,1,-1,0,0,1,1,0,0,-1,0,0,
-1,0,0,0,0,0,0,1,0,-1,1,0,1,0,0,1,0,1,0,-1,-1,-1,1,-1,0,0,-1,0,-1,
-1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
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,-1,0,1,0,1,0,0,0,-2,-3,-1,1,1,-1,0,0,1,1,1,0,2,-1,0,0,1,1,-1,0,
1,-1,0,-1,-3,1,1,0,0,1,-2,1,-1,2,-1,-2,-1,-1,0,1,1,0,-1,0,1,1,1,
1,1,2,-1,0,0,1,-2,-1,-1,0,2,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
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,
-1,-1,-1,1,-3,1,2,-4,-3,-8,-15,-3,4,-2,-2,1,0,6,3,4,-2,6,-2,-4,0,
5,-1,-2,1,1,-3,2,-2,-13,2,-1,-4,1,2,-11,3,-4,3,-3,-5,-2,-4,3,2,1,
-3,-2,1,1,2,8,3,3,5,-1,-5,0,7,-8,-3,-4,-1,6,
1,-1,-2,3,-9,3,5,-10,-6,-15,-30,-6,6,-4,-5,1,-2,13,5,7,-6,14,-4,-7,
0,12,-2,-7,0,2,-7,6,-5,-27,5,-4,-9,1,4,-23,6,-9,8,-8,-12,-4,-10,
9,7,3,-6,-5,1,1,8,16,3,7,12,-7,-8,2,15,-15,-5,-8,-2,11,
-2,0,-8,2,-19,8,11,-25,-19,-36,-70,-14,17,-9,-15,6,-6,30,11,17,-14,
33,-7,-17,2,26,-2,-15,0,0,-17,14,-14,-64,10,-9,-21,5,5,-54,19,-20,
22,-23,-24,-9,-20,17,13,7,-15,-8,-1,-1,17,37,13,14,26,-13,-21,5,
33,-40,-14,-18,-6,28,
0,1,3,-2,8,-4,-4,9,7,14,27,6,-6,3,6,-1,3,-12,-4,-7,6,-13,4,6,0,-10,
1,7,1,-1,8,-5,6,25,-4,3,8,-1,-3,21,-7,8,-9,9,11,4,9,-7,-6,-3,6,4,
0,0,-8,-14,-4,-7,-11,7,7,-2,-13,15,5,7,3,-11,
0,1,0,0,-1,0,1,-2,0,-1,-4,0,1,-1,0,1,0,2,0,1,0,2,0,-2,1,1,0,0,1,0,
0,1,0,-2,0,-1,-2,1,0,-3,1,-1,0,-1,0,0,0,2,0,0,0,0,0,0,0,3,1,-1,0,
2,-2,0,2,-2,-1,0,1,1,
0,1,3,-2,8,-4,-4,9,7,14,27,6,-6,3,6,-1,3,-12,-4,-7,6,-13,4,6,0,-10,
1,7,1,-1,8,-5,6,26,-4,3,8,-1,-3,21,-7,8,-9,9,11,4,9,-7,-6,-3,6,4,
0,0,-8,-14,-4,-7,-11,7,7,-2,-13,15,5,7,3,-11,
0,1,2,-1,7,-4,-4,7,6,12,24,5,-6,3,5,-1,3,-11,-4,-5,6,-11,3,4,0,-9,
0,6,1,-1,7,-5,5,23,-3,2,6,0,-2,18,-7,6,-8,8,9,4,7,-7,-6,-3,5,3,0,
-1,-6,-13,-4,-6,-9,6,6,-2,-12,14,4,6,2,-10,
1,-1,2,1,1,0,0,3,3,2,4,1,-1,1,1,-1,1,-2,0,-1,1,-2,0,1,0,-1,1,1,0,
2,1,-1,2,4,0,1,2,-1,1,4,-2,1,-2,3,0,0,1,0,0,0,2,0,1,1,-1,-2,-2,0,
-1,0,2,0,-1,3,1,1,1,-2,
-1,1,-2,-1,-1,0,0,-3,-3,-2,-4,-1,1,-1,-1,1,-1,2,0,1,-1,2,0,-1,0,1,
-1,-1,0,-2,-1,1,-1,-4,0,-1,-2,1,-1,-4,2,-1,2,-3,0,0,-1,0,0,0,-2,
0,-1,-1,1,2,2,0,1,0,-2,0,1,-3,-1,-1,-1,2,
0,0,-6,2,-15,5,8,-19,-14,-25,-50,-10,11,-7,-11,3,-5,22,7,11,-11,24,
-5,-11,1,19,-2,-12,-1,0,-12,11,-10,-46,7,-7,-15,3,3,-39,13,-14,16,
-17,-18,-7,-15,14,11,5,-11,-7,-1,-1,13,27,8,10,19,-11,-14,4,24,-28,
-9,-13,-4,19,
-1,0,-4,3,-10,5,6,-13,-9,-21,-40,-7,9,-5,-8,3,-3,17,7,10,-7,19,-5,
-10,1,15,-1,-8,1,1,-10,7,-7,-36,6,-5,-12,2,5,-31,10,-12,12,-12,-15,
-5,-12,10,7,4,-8,-5,1,0,10,21,7,9,15,-7,-12,2,19,-22,-8,-10,-3,16,
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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,
0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,
1,0,1,0,3,-1,-2,4,4,6,13,2,-4,2,3,-2,1,-6,-3,-3,2,-6,1,3,-1,-5,1,
2,-1,0,3,-2,2,12,-2,1,4,-1,-1,10,-4,3,-3,4,4,1,3,-3,-1,-1,3,0,0,
0,-2,-7,-4,-2,-4,1,5,0,-6,8,3,3,1,-6]>;

return _LR;
