Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} + 4x^{2} + 1 \)
| $\times$ | \(\chi_{ 24 } ( 1, ·)\) | \(\chi_{ 24 } ( 19, ·)\) | \(\chi_{ 24 } ( 5, ·)\) | \(\chi_{ 24 } ( 23, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 24 }(1, ·)\) | \(\chi_{ 24 } ( 1, ·)\) | \(\chi_{ 24 } ( 19, ·)\) | \(\chi_{ 24 } ( 5, ·)\) | \(\chi_{ 24 } ( 23, ·)\) |
| \(\chi_{ 24 }(19, ·)\) | \(\chi_{ 24 } ( 19, ·)\) | \(\chi_{ 24 } ( 1, ·)\) | \(\chi_{ 24 } ( 23, ·)\) | \(\chi_{ 24 } ( 5, ·)\) |
| \(\chi_{ 24 }(5, ·)\) | \(\chi_{ 24 } ( 5, ·)\) | \(\chi_{ 24 } ( 23, ·)\) | \(\chi_{ 24 } ( 1, ·)\) | \(\chi_{ 24 } ( 19, ·)\) |
| \(\chi_{ 24 }(23, ·)\) | \(\chi_{ 24 } ( 23, ·)\) | \(\chi_{ 24 } ( 5, ·)\) | \(\chi_{ 24 } ( 19, ·)\) | \(\chi_{ 24 } ( 1, ·)\) |