Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} - 2x^{3} + 17x^{2} - 16x + 22 \)
| $\times$ | \(\chi_{ 168 } ( 1, ·)\) | \(\chi_{ 168 } ( 97, ·)\) | \(\chi_{ 168 } ( 29, ·)\) | \(\chi_{ 168 } ( 125, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 168 }(1, ·)\) | \(\chi_{ 168 } ( 1, ·)\) | \(\chi_{ 168 } ( 97, ·)\) | \(\chi_{ 168 } ( 29, ·)\) | \(\chi_{ 168 } ( 125, ·)\) |
| \(\chi_{ 168 }(97, ·)\) | \(\chi_{ 168 } ( 97, ·)\) | \(\chi_{ 168 } ( 1, ·)\) | \(\chi_{ 168 } ( 125, ·)\) | \(\chi_{ 168 } ( 29, ·)\) |
| \(\chi_{ 168 }(29, ·)\) | \(\chi_{ 168 } ( 29, ·)\) | \(\chi_{ 168 } ( 125, ·)\) | \(\chi_{ 168 } ( 1, ·)\) | \(\chi_{ 168 } ( 97, ·)\) |
| \(\chi_{ 168 }(125, ·)\) | \(\chi_{ 168 } ( 125, ·)\) | \(\chi_{ 168 } ( 29, ·)\) | \(\chi_{ 168 } ( 97, ·)\) | \(\chi_{ 168 } ( 1, ·)\) |