Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{6} - 9 x^{4} - 4 x^{3} + 9 x^{2} + 3 x - 1 \)
| $\times$ | \(\chi_{ 45 } ( 1, ·)\) | \(\chi_{ 45 } ( 16, ·)\) | \(\chi_{ 45 } ( 34, ·)\) | \(\chi_{ 45 } ( 19, ·)\) | \(\chi_{ 45 } ( 4, ·)\) | \(\chi_{ 45 } ( 31, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 45 }(1, ·)\) | \(\chi_{ 45 } ( 1, ·)\) | \(\chi_{ 45 } ( 16, ·)\) | \(\chi_{ 45 } ( 34, ·)\) | \(\chi_{ 45 } ( 19, ·)\) | \(\chi_{ 45 } ( 4, ·)\) | \(\chi_{ 45 } ( 31, ·)\) |
| \(\chi_{ 45 }(16, ·)\) | \(\chi_{ 45 } ( 16, ·)\) | \(\chi_{ 45 } ( 31, ·)\) | \(\chi_{ 45 } ( 4, ·)\) | \(\chi_{ 45 } ( 34, ·)\) | \(\chi_{ 45 } ( 19, ·)\) | \(\chi_{ 45 } ( 1, ·)\) |
| \(\chi_{ 45 }(34, ·)\) | \(\chi_{ 45 } ( 34, ·)\) | \(\chi_{ 45 } ( 4, ·)\) | \(\chi_{ 45 } ( 31, ·)\) | \(\chi_{ 45 } ( 16, ·)\) | \(\chi_{ 45 } ( 1, ·)\) | \(\chi_{ 45 } ( 19, ·)\) |
| \(\chi_{ 45 }(19, ·)\) | \(\chi_{ 45 } ( 19, ·)\) | \(\chi_{ 45 } ( 34, ·)\) | \(\chi_{ 45 } ( 16, ·)\) | \(\chi_{ 45 } ( 1, ·)\) | \(\chi_{ 45 } ( 31, ·)\) | \(\chi_{ 45 } ( 4, ·)\) |
| \(\chi_{ 45 }(4, ·)\) | \(\chi_{ 45 } ( 4, ·)\) | \(\chi_{ 45 } ( 19, ·)\) | \(\chi_{ 45 } ( 1, ·)\) | \(\chi_{ 45 } ( 31, ·)\) | \(\chi_{ 45 } ( 16, ·)\) | \(\chi_{ 45 } ( 34, ·)\) |
| \(\chi_{ 45 }(31, ·)\) | \(\chi_{ 45 } ( 31, ·)\) | \(\chi_{ 45 } ( 1, ·)\) | \(\chi_{ 45 } ( 19, ·)\) | \(\chi_{ 45 } ( 4, ·)\) | \(\chi_{ 45 } ( 34, ·)\) | \(\chi_{ 45 } ( 16, ·)\) |