Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{4} - x^{3} + 51 x^{2} - 51 x + 551 \)
| $\times$ | \(\chi_{ 205 } ( 1, ·)\) | \(\chi_{ 205 } ( 122, ·)\) | \(\chi_{ 205 } ( 163, ·)\) | \(\chi_{ 205 } ( 124, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 205 }(1, ·)\) | \(\chi_{ 205 } ( 1, ·)\) | \(\chi_{ 205 } ( 122, ·)\) | \(\chi_{ 205 } ( 163, ·)\) | \(\chi_{ 205 } ( 124, ·)\) |
| \(\chi_{ 205 }(122, ·)\) | \(\chi_{ 205 } ( 122, ·)\) | \(\chi_{ 205 } ( 124, ·)\) | \(\chi_{ 205 } ( 1, ·)\) | \(\chi_{ 205 } ( 163, ·)\) |
| \(\chi_{ 205 }(163, ·)\) | \(\chi_{ 205 } ( 163, ·)\) | \(\chi_{ 205 } ( 1, ·)\) | \(\chi_{ 205 } ( 124, ·)\) | \(\chi_{ 205 } ( 122, ·)\) |
| \(\chi_{ 205 }(124, ·)\) | \(\chi_{ 205 } ( 124, ·)\) | \(\chi_{ 205 } ( 163, ·)\) | \(\chi_{ 205 } ( 122, ·)\) | \(\chi_{ 205 } ( 1, ·)\) |