Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{6} \) \(\mathstrut -\mathstrut x^{5} \) \(\mathstrut -\mathstrut 6 x^{4} \) \(\mathstrut +\mathstrut 6 x^{3} \) \(\mathstrut +\mathstrut 8 x^{2} \) \(\mathstrut -\mathstrut 8 x \) \(\mathstrut +\mathstrut 1 \)
| $\times$ | \(\chi_{ 21 } ( 1, ·)\) | \(\chi_{ 21 } ( 16, ·)\) | \(\chi_{ 21 } ( 4, ·)\) | \(\chi_{ 21 } ( 5, ·)\) | \(\chi_{ 21 } ( 17, ·)\) | \(\chi_{ 21 } ( 20, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 21 }(1, ·)\) | \(\chi_{ 21 } ( 1, ·)\) | \(\chi_{ 21 } ( 16, ·)\) | \(\chi_{ 21 } ( 4, ·)\) | \(\chi_{ 21 } ( 5, ·)\) | \(\chi_{ 21 } ( 17, ·)\) | \(\chi_{ 21 } ( 20, ·)\) |
| \(\chi_{ 21 }(16, ·)\) | \(\chi_{ 21 } ( 16, ·)\) | \(\chi_{ 21 } ( 4, ·)\) | \(\chi_{ 21 } ( 1, ·)\) | \(\chi_{ 21 } ( 17, ·)\) | \(\chi_{ 21 } ( 20, ·)\) | \(\chi_{ 21 } ( 5, ·)\) |
| \(\chi_{ 21 }(4, ·)\) | \(\chi_{ 21 } ( 4, ·)\) | \(\chi_{ 21 } ( 1, ·)\) | \(\chi_{ 21 } ( 16, ·)\) | \(\chi_{ 21 } ( 20, ·)\) | \(\chi_{ 21 } ( 5, ·)\) | \(\chi_{ 21 } ( 17, ·)\) |
| \(\chi_{ 21 }(5, ·)\) | \(\chi_{ 21 } ( 5, ·)\) | \(\chi_{ 21 } ( 17, ·)\) | \(\chi_{ 21 } ( 20, ·)\) | \(\chi_{ 21 } ( 4, ·)\) | \(\chi_{ 21 } ( 1, ·)\) | \(\chi_{ 21 } ( 16, ·)\) |
| \(\chi_{ 21 }(17, ·)\) | \(\chi_{ 21 } ( 17, ·)\) | \(\chi_{ 21 } ( 20, ·)\) | \(\chi_{ 21 } ( 5, ·)\) | \(\chi_{ 21 } ( 1, ·)\) | \(\chi_{ 21 } ( 16, ·)\) | \(\chi_{ 21 } ( 4, ·)\) |
| \(\chi_{ 21 }(20, ·)\) | \(\chi_{ 21 } ( 20, ·)\) | \(\chi_{ 21 } ( 5, ·)\) | \(\chi_{ 21 } ( 17, ·)\) | \(\chi_{ 21 } ( 16, ·)\) | \(\chi_{ 21 } ( 4, ·)\) | \(\chi_{ 21 } ( 1, ·)\) |