Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{6} \) \(\mathstrut -\mathstrut x^{5} \) \(\mathstrut +\mathstrut 3 x^{4} \) \(\mathstrut -\mathstrut 11 x^{3} \) \(\mathstrut +\mathstrut 44 x^{2} \) \(\mathstrut -\mathstrut 36 x \) \(\mathstrut +\mathstrut 32 \)
| $\times$ | \(\chi_{ 31 } ( 1, ·)\) | \(\chi_{ 31 } ( 5, ·)\) | \(\chi_{ 31 } ( 6, ·)\) | \(\chi_{ 31 } ( 25, ·)\) | \(\chi_{ 31 } ( 26, ·)\) | \(\chi_{ 31 } ( 30, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 31 }(1, ·)\) | \(\chi_{ 31 } ( 1, ·)\) | \(\chi_{ 31 } ( 5, ·)\) | \(\chi_{ 31 } ( 6, ·)\) | \(\chi_{ 31 } ( 25, ·)\) | \(\chi_{ 31 } ( 26, ·)\) | \(\chi_{ 31 } ( 30, ·)\) |
| \(\chi_{ 31 }(5, ·)\) | \(\chi_{ 31 } ( 5, ·)\) | \(\chi_{ 31 } ( 25, ·)\) | \(\chi_{ 31 } ( 30, ·)\) | \(\chi_{ 31 } ( 1, ·)\) | \(\chi_{ 31 } ( 6, ·)\) | \(\chi_{ 31 } ( 26, ·)\) |
| \(\chi_{ 31 }(6, ·)\) | \(\chi_{ 31 } ( 6, ·)\) | \(\chi_{ 31 } ( 30, ·)\) | \(\chi_{ 31 } ( 5, ·)\) | \(\chi_{ 31 } ( 26, ·)\) | \(\chi_{ 31 } ( 1, ·)\) | \(\chi_{ 31 } ( 25, ·)\) |
| \(\chi_{ 31 }(25, ·)\) | \(\chi_{ 31 } ( 25, ·)\) | \(\chi_{ 31 } ( 1, ·)\) | \(\chi_{ 31 } ( 26, ·)\) | \(\chi_{ 31 } ( 5, ·)\) | \(\chi_{ 31 } ( 30, ·)\) | \(\chi_{ 31 } ( 6, ·)\) |
| \(\chi_{ 31 }(26, ·)\) | \(\chi_{ 31 } ( 26, ·)\) | \(\chi_{ 31 } ( 6, ·)\) | \(\chi_{ 31 } ( 1, ·)\) | \(\chi_{ 31 } ( 30, ·)\) | \(\chi_{ 31 } ( 25, ·)\) | \(\chi_{ 31 } ( 5, ·)\) |
| \(\chi_{ 31 }(30, ·)\) | \(\chi_{ 31 } ( 30, ·)\) | \(\chi_{ 31 } ( 26, ·)\) | \(\chi_{ 31 } ( 25, ·)\) | \(\chi_{ 31 } ( 6, ·)\) | \(\chi_{ 31 } ( 5, ·)\) | \(\chi_{ 31 } ( 1, ·)\) |