local result;

result := rec();

result.comment := "S4(9) as 41 x 41 matrices (b) over Z\n\n\
Note that the representations 41a and 41b can be distinguished by\n\
considering the element x*y^3*x*y^2*(x*y)^3; its trace\n\
is respectively -2 and 1.\n";

result.symmetricforms := [ ];

result.antisymmetricforms := [ ];

result.hermitianforms := [ ];

result.centralizeralgebra := [ ];

result.generators := [
[[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],
[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],
[0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
  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],
[0,0,0,0,1,0,0,0,0,1,0,-1,-1,0,0,0,0,0,0,0,1,0,0,-1,0,-1,0,0,1,-1,
  0,0,1,0,-1,1,0,0,1,0,0],
[1,0,-2,0,-1,-1,1,0,0,2,1,0,-2,-1,1,1,-1,0,1,1,2,0,-1,0,-1,0,1,0,0,
  -2,-2,1,0,0,-1,1,-1,1,0,0,0],
[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,-1,0,0,0,1,-1,0,2,0,-1,-1,-1,0,1,0,0,0,1,1,0,-1,0,0,0,0,0,1,-2,
  -1,1,1,0,0,1,0,0,0,1,1],
[0,0,1,1,1,0,-1,0,0,-1,-1,0,0,1,0,-1,0,1,0,0,-1,1,1,0,0,0,-1,1,0,1,
  1,0,-1,-1,0,0,1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[1,1,0,1,0,1,0,-1,0,-2,1,-1,-1,0,-1,-1,0,-1,-1,0,-3,1,0,0,0,0,-3,3,
  1,0,2,-2,-2,-1,1,0,1,0,0,1,1],
[1,1,1,1,0,0,-1,0,0,-3,0,0,-1,1,-1,-1,0,0,-1,-1,-3,1,1,0,0,0,-2,3,
  -1,2,2,-2,-3,-1,1,-1,1,0,0,0,0],
[0,0,1,1,1,0,-1,0,0,-1,-1,0,1,1,0,-1,0,0,0,0,-1,1,1,0,0,0,-1,0,0,1,
  1,0,0,-1,0,0,1,0,0,0,0],
[0,0,0,0,0,0,1,0,0,0,0,0,-1,-1,0,0,0,0,0,1,-1,1,-1,0,0,0,0,1,0,0,0,
  0,-1,-1,1,0,0,0,0,0,1],
[1,0,0,1,0,1,0,-1,1,0,0,-1,-1,0,-1,-1,0,0,-1,1,-1,2,0,0,0,0,-2,2,2,
  -1,1,0,-1,-2,1,0,1,1,0,1,2],
[1,0,-2,0,0,0,1,-1,1,2,1,-1,-2,-1,-1,0,0,0,0,1,0,2,-1,0,0,-1,-1,2,
  2,-3,0,0,0,-1,0,1,0,1,0,1,2],
[-1,-1,-2,0,-1,0,1,0,-1,4,0,0,-1,-2,1,3,-1,0,1,2,3,-1,-2,0,0,0,3,-2,
  1,-3,-3,3,3,0,0,1,-1,0,0,0,1],
[1,-1,-1,1,0,0,1,-1,0,2,1,-1,-2,-2,0,0,-1,0,0,2,0,2,-1,0,0,0,-1,1,
  1,-3,-1,1,0,-2,1,1,0,1,0,1,2],
[0,0,0,0,0,0,0,1,0,0,0,-1,-1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,
  0,0,0,0,0,0,0,1,0],
[-1,0,0,-2,0,-1,1,1,0,0,0,1,1,-1,0,1,1,0,1,0,0,-1,-1,0,0,0,2,-2,-1,
  0,-1,0,1,2,0,0,-1,-1,0,-1,-1]]
,
[[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],
[0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[-1,0,0,-1,0,0,0,0,0,0,0,1,1,0,0,1,1,0,1,0,-1,0,0,0,0,0,1,0,-1,1,0,
  0,0,1,0,0,0,-1,-1,-1,0],
[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],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
  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],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,-1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,-1,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,-1,0,0,-1,0,0,1,0,0,-1,0,-1,
  0,1,0,0,1,0,0,0,1,0,0],
[-1,1,0,0,-1,-1,-1,0,0,0,0,2,2,1,0,0,1,0,0,0,0,-1,0,1,0,1,1,-1,-1,
  1,0,0,0,2,-1,-1,0,0,-1,0,-1],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,-1,0,0,0,0,1,-1,0,-1,-1,
  1,1,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
  0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,-1,0,0,0,0,-1,1,0,0,0,0,-1,1,0,1,0,
  -1,-1,0,0,0,1,0,0,0,0],
[0,1,3,1,1,1,-1,0,1,-5,0,0,1,1,-1,-3,1,0,-1,-2,-5,1,2,0,0,0,-3,2,-1,
  3,3,-3,-3,0,1,-1,2,-1,0,0,-1],
[-1,-2,-2,0,-1,-2,1,-1,-1,7,0,1,0,-2,1,3,-1,1,2,3,6,0,-2,1,-1,0,4,
  -4,1,-4,-4,5,4,0,-1,1,-2,1,-1,0,1],
[-2,-1,1,0,0,-1,0,-1,0,1,0,2,2,-1,0,0,0,1,2,2,0,1,0,1,-1,0,1,-3,-1,
  0,-1,2,1,1,0,1,0,-1,-1,-1,-1],
[1,0,0,1,-1,0,0,0,0,-1,0,-1,-1,1,0,0,0,0,-1,0,0,0,0,0,0,0,-1,2,1,0,
  1,-1,-1,-1,0,-1,0,1,0,1,1],
[0,1,2,-1,0,1,-1,1,1,-4,0,0,1,1,-1,-1,1,0,-1,-2,-2,0,1,-1,0,0,-1,2,
  -1,3,2,-3,-2,1,0,-1,1,-1,0,0,-1],
[-1,0,1,-1,0,1,0,2,0,-2,-1,-1,1,1,0,1,1,0,-1,-2,0,-2,0,-1,0,0,1,1,
  -1,3,1,-2,0,1,0,-2,0,-1,0,0,0],
[1,2,1,1,0,1,-1,0,1,-3,0,-1,0,1,-1,-2,1,0,-1,-2,-2,0,1,0,0,0,-2,2,
  0,1,2,-2,-2,0,0,-1,1,0,0,1,0],
[1,2,2,1,1,0,-2,-1,1,-4,1,0,1,3,-2,-3,1,0,-2,-2,-3,1,2,0,0,0,-3,3,
  0,2,3,-3,-3,0,0,-1,2,1,0,0,-1],
[0,1,2,0,0,1,-1,0,1,-4,0,0,1,1,-1,-1,1,0,-1,-2,-3,0,1,0,0,0,-1,1,-1,
  2,2,-2,-2,0,1,-1,1,-1,0,0,-1],
[-1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,
  1,1,-1,0,0,0,0,0,0],
[0,1,2,0,0,1,-1,0,1,-4,0,0,1,1,-1,-1,1,0,-1,-2,-3,0,2,0,0,0,-1,1,-1,
  2,2,-2,-2,0,1,-1,1,-1,0,0,-1],
[1,2,1,1,0,1,-1,0,1,-3,0,0,0,1,-1,-2,1,0,-1,-2,-2,0,1,0,0,0,-2,2,0,
  1,2,-2,-2,0,0,-1,1,0,0,1,0]]];

return result;