Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{6} \) \(\mathstrut +\mathstrut 6 x^{4} \) \(\mathstrut -\mathstrut 4 x^{3} \) \(\mathstrut +\mathstrut 9 x^{2} \) \(\mathstrut -\mathstrut 12 x \) \(\mathstrut +\mathstrut 19 \)
| $\times$ | \(\chi_{ 45 } ( 1, ·)\) | \(\chi_{ 45 } ( 16, ·)\) | \(\chi_{ 45 } ( 44, ·)\) | \(\chi_{ 45 } ( 29, ·)\) | \(\chi_{ 45 } ( 14, ·)\) | \(\chi_{ 45 } ( 31, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 45 }(1, ·)\) | \(\chi_{ 45 } ( 1, ·)\) | \(\chi_{ 45 } ( 16, ·)\) | \(\chi_{ 45 } ( 44, ·)\) | \(\chi_{ 45 } ( 29, ·)\) | \(\chi_{ 45 } ( 14, ·)\) | \(\chi_{ 45 } ( 31, ·)\) |
| \(\chi_{ 45 }(16, ·)\) | \(\chi_{ 45 } ( 16, ·)\) | \(\chi_{ 45 } ( 31, ·)\) | \(\chi_{ 45 } ( 29, ·)\) | \(\chi_{ 45 } ( 14, ·)\) | \(\chi_{ 45 } ( 44, ·)\) | \(\chi_{ 45 } ( 1, ·)\) |
| \(\chi_{ 45 }(44, ·)\) | \(\chi_{ 45 } ( 44, ·)\) | \(\chi_{ 45 } ( 29, ·)\) | \(\chi_{ 45 } ( 1, ·)\) | \(\chi_{ 45 } ( 16, ·)\) | \(\chi_{ 45 } ( 31, ·)\) | \(\chi_{ 45 } ( 14, ·)\) |
| \(\chi_{ 45 }(29, ·)\) | \(\chi_{ 45 } ( 29, ·)\) | \(\chi_{ 45 } ( 14, ·)\) | \(\chi_{ 45 } ( 16, ·)\) | \(\chi_{ 45 } ( 31, ·)\) | \(\chi_{ 45 } ( 1, ·)\) | \(\chi_{ 45 } ( 44, ·)\) |
| \(\chi_{ 45 }(14, ·)\) | \(\chi_{ 45 } ( 14, ·)\) | \(\chi_{ 45 } ( 44, ·)\) | \(\chi_{ 45 } ( 31, ·)\) | \(\chi_{ 45 } ( 1, ·)\) | \(\chi_{ 45 } ( 16, ·)\) | \(\chi_{ 45 } ( 29, ·)\) |
| \(\chi_{ 45 }(31, ·)\) | \(\chi_{ 45 } ( 31, ·)\) | \(\chi_{ 45 } ( 1, ·)\) | \(\chi_{ 45 } ( 14, ·)\) | \(\chi_{ 45 } ( 44, ·)\) | \(\chi_{ 45 } ( 29, ·)\) | \(\chi_{ 45 } ( 16, ·)\) |