Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 \)
| $\times$ | \(\chi_{ 11 } ( 1, ·)\) | \(\chi_{ 11 } ( 3, ·)\) | \(\chi_{ 11 } ( 4, ·)\) | \(\chi_{ 11 } ( 5, ·)\) | \(\chi_{ 11 } ( 9, ·)\) |
|---|---|---|---|---|---|
| \(\chi_{ 11 }(1, ·)\) | \(\chi_{ 11 } ( 1, ·)\) | \(\chi_{ 11 } ( 3, ·)\) | \(\chi_{ 11 } ( 4, ·)\) | \(\chi_{ 11 } ( 5, ·)\) | \(\chi_{ 11 } ( 9, ·)\) |
| \(\chi_{ 11 }(3, ·)\) | \(\chi_{ 11 } ( 3, ·)\) | \(\chi_{ 11 } ( 9, ·)\) | \(\chi_{ 11 } ( 1, ·)\) | \(\chi_{ 11 } ( 4, ·)\) | \(\chi_{ 11 } ( 5, ·)\) |
| \(\chi_{ 11 }(4, ·)\) | \(\chi_{ 11 } ( 4, ·)\) | \(\chi_{ 11 } ( 1, ·)\) | \(\chi_{ 11 } ( 5, ·)\) | \(\chi_{ 11 } ( 9, ·)\) | \(\chi_{ 11 } ( 3, ·)\) |
| \(\chi_{ 11 }(5, ·)\) | \(\chi_{ 11 } ( 5, ·)\) | \(\chi_{ 11 } ( 4, ·)\) | \(\chi_{ 11 } ( 9, ·)\) | \(\chi_{ 11 } ( 3, ·)\) | \(\chi_{ 11 } ( 1, ·)\) |
| \(\chi_{ 11 }(9, ·)\) | \(\chi_{ 11 } ( 9, ·)\) | \(\chi_{ 11 } ( 5, ·)\) | \(\chi_{ 11 } ( 3, ·)\) | \(\chi_{ 11 } ( 1, ·)\) | \(\chi_{ 11 } ( 4, ·)\) |