Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} - x^{3} - 14x^{2} + 14x + 31 \)
| $\times$ | \(\chi_{ 55 } ( 1, ·)\) | \(\chi_{ 55 } ( 32, ·)\) | \(\chi_{ 55 } ( 34, ·)\) | \(\chi_{ 55 } ( 43, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 55 }(1, ·)\) | \(\chi_{ 55 } ( 1, ·)\) | \(\chi_{ 55 } ( 32, ·)\) | \(\chi_{ 55 } ( 34, ·)\) | \(\chi_{ 55 } ( 43, ·)\) |
| \(\chi_{ 55 }(32, ·)\) | \(\chi_{ 55 } ( 32, ·)\) | \(\chi_{ 55 } ( 34, ·)\) | \(\chi_{ 55 } ( 43, ·)\) | \(\chi_{ 55 } ( 1, ·)\) |
| \(\chi_{ 55 }(34, ·)\) | \(\chi_{ 55 } ( 34, ·)\) | \(\chi_{ 55 } ( 43, ·)\) | \(\chi_{ 55 } ( 1, ·)\) | \(\chi_{ 55 } ( 32, ·)\) |
| \(\chi_{ 55 }(43, ·)\) | \(\chi_{ 55 } ( 43, ·)\) | \(\chi_{ 55 } ( 1, ·)\) | \(\chi_{ 55 } ( 32, ·)\) | \(\chi_{ 55 } ( 34, ·)\) |