# Character: X5
# Comment: perm rep on 253 pts (cosets of S4)
# Ind: 1
# Ring: Z
# Sparsity: 69%
# Maximum absolute entry: 7
# Checker result: pass
# Conjugacy class representative result: pass

local a, A, b, B, c, C, w, W, i, result, delta, idmat;

result := rec();

w := E(3); W := E(3)^2;
a := E(5)+E(5)^4; A := -1-a; # b5, b5*
b := E(7)+E(7)^2+E(7)^4; B := -1-b;  # b7, b7**
c := E(11)+E(11)^3+E(11)^4+E(11)^5+E(11)^9; C := -1-c; # b11, b11**
i := E(4);
result.comment := "L223 as 22 x 22 matrices\n";

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

return result;