Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{4} + 2 x^{2} + 4 \)
| $\times$ | \(\chi_{ 24 } ( 1, ·)\) | \(\chi_{ 24 } ( 5, ·)\) | \(\chi_{ 24 } ( 13, ·)\) | \(\chi_{ 24 } ( 17, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 24 }(1, ·)\) | \(\chi_{ 24 } ( 1, ·)\) | \(\chi_{ 24 } ( 5, ·)\) | \(\chi_{ 24 } ( 13, ·)\) | \(\chi_{ 24 } ( 17, ·)\) |
| \(\chi_{ 24 }(5, ·)\) | \(\chi_{ 24 } ( 5, ·)\) | \(\chi_{ 24 } ( 1, ·)\) | \(\chi_{ 24 } ( 17, ·)\) | \(\chi_{ 24 } ( 13, ·)\) |
| \(\chi_{ 24 }(13, ·)\) | \(\chi_{ 24 } ( 13, ·)\) | \(\chi_{ 24 } ( 17, ·)\) | \(\chi_{ 24 } ( 1, ·)\) | \(\chi_{ 24 } ( 5, ·)\) |
| \(\chi_{ 24 }(17, ·)\) | \(\chi_{ 24 } ( 17, ·)\) | \(\chi_{ 24 } ( 13, ·)\) | \(\chi_{ 24 } ( 5, ·)\) | \(\chi_{ 24 } ( 1, ·)\) |