Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{8} - x^{4} + 1\) 
| $\times$ | \(\chi_{ 24 } ( 1, ·)\) | \(\chi_{ 24 } ( 5, ·)\) | \(\chi_{ 24 } ( 7, ·)\) | \(\chi_{ 24 } ( 11, ·)\) | \(\chi_{ 24 } ( 13, ·)\) | \(\chi_{ 24 } ( 17, ·)\) | \(\chi_{ 24 } ( 19, ·)\) | \(\chi_{ 24 } ( 23, ·)\) |
|---|---|---|---|---|---|---|---|---|
| \(\chi_{ 24 }(1, ·)\) | \(\chi_{ 24 } ( 1, ·)\) | \(\chi_{ 24 } ( 5, ·)\) | \(\chi_{ 24 } ( 7, ·)\) | \(\chi_{ 24 } ( 11, ·)\) | \(\chi_{ 24 } ( 13, ·)\) | \(\chi_{ 24 } ( 17, ·)\) | \(\chi_{ 24 } ( 19, ·)\) | \(\chi_{ 24 } ( 23, ·)\) |
| \(\chi_{ 24 }(5, ·)\) | \(\chi_{ 24 } ( 5, ·)\) | \(\chi_{ 24 } ( 1, ·)\) | \(\chi_{ 24 } ( 11, ·)\) | \(\chi_{ 24 } ( 7, ·)\) | \(\chi_{ 24 } ( 17, ·)\) | \(\chi_{ 24 } ( 13, ·)\) | \(\chi_{ 24 } ( 23, ·)\) | \(\chi_{ 24 } ( 19, ·)\) |
| \(\chi_{ 24 }(7, ·)\) | \(\chi_{ 24 } ( 7, ·)\) | \(\chi_{ 24 } ( 11, ·)\) | \(\chi_{ 24 } ( 1, ·)\) | \(\chi_{ 24 } ( 5, ·)\) | \(\chi_{ 24 } ( 19, ·)\) | \(\chi_{ 24 } ( 23, ·)\) | \(\chi_{ 24 } ( 13, ·)\) | \(\chi_{ 24 } ( 17, ·)\) |
| \(\chi_{ 24 }(11, ·)\) | \(\chi_{ 24 } ( 11, ·)\) | \(\chi_{ 24 } ( 7, ·)\) | \(\chi_{ 24 } ( 5, ·)\) | \(\chi_{ 24 } ( 1, ·)\) | \(\chi_{ 24 } ( 23, ·)\) | \(\chi_{ 24 } ( 19, ·)\) | \(\chi_{ 24 } ( 17, ·)\) | \(\chi_{ 24 } ( 13, ·)\) |
| \(\chi_{ 24 }(13, ·)\) | \(\chi_{ 24 } ( 13, ·)\) | \(\chi_{ 24 } ( 17, ·)\) | \(\chi_{ 24 } ( 19, ·)\) | \(\chi_{ 24 } ( 23, ·)\) | \(\chi_{ 24 } ( 1, ·)\) | \(\chi_{ 24 } ( 5, ·)\) | \(\chi_{ 24 } ( 7, ·)\) | \(\chi_{ 24 } ( 11, ·)\) |
| \(\chi_{ 24 }(17, ·)\) | \(\chi_{ 24 } ( 17, ·)\) | \(\chi_{ 24 } ( 13, ·)\) | \(\chi_{ 24 } ( 23, ·)\) | \(\chi_{ 24 } ( 19, ·)\) | \(\chi_{ 24 } ( 5, ·)\) | \(\chi_{ 24 } ( 1, ·)\) | \(\chi_{ 24 } ( 11, ·)\) | \(\chi_{ 24 } ( 7, ·)\) |
| \(\chi_{ 24 }(19, ·)\) | \(\chi_{ 24 } ( 19, ·)\) | \(\chi_{ 24 } ( 23, ·)\) | \(\chi_{ 24 } ( 13, ·)\) | \(\chi_{ 24 } ( 17, ·)\) | \(\chi_{ 24 } ( 7, ·)\) | \(\chi_{ 24 } ( 11, ·)\) | \(\chi_{ 24 } ( 1, ·)\) | \(\chi_{ 24 } ( 5, ·)\) |
| \(\chi_{ 24 }(23, ·)\) | \(\chi_{ 24 } ( 23, ·)\) | \(\chi_{ 24 } ( 19, ·)\) | \(\chi_{ 24 } ( 17, ·)\) | \(\chi_{ 24 } ( 13, ·)\) | \(\chi_{ 24 } ( 11, ·)\) | \(\chi_{ 24 } ( 7, ·)\) | \(\chi_{ 24 } ( 5, ·)\) | \(\chi_{ 24 } ( 1, ·)\) |