Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{6} \) \(\mathstrut -\mathstrut 14 x^{4} \) \(\mathstrut +\mathstrut 56 x^{2} \) \(\mathstrut -\mathstrut 56 \)
| $\times$ | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 19, ·)\) | \(\chi_{ 56 } ( 3, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 27, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 56 }(1, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 19, ·)\) | \(\chi_{ 56 } ( 3, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 27, ·)\) |
| \(\chi_{ 56 }(19, ·)\) | \(\chi_{ 56 } ( 19, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 27, ·)\) | \(\chi_{ 56 } ( 3, ·)\) | \(\chi_{ 56 } ( 9, ·)\) |
| \(\chi_{ 56 }(3, ·)\) | \(\chi_{ 56 } ( 3, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 19, ·)\) | \(\chi_{ 56 } ( 27, ·)\) | \(\chi_{ 56 } ( 25, ·)\) |
| \(\chi_{ 56 }(25, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 27, ·)\) | \(\chi_{ 56 } ( 19, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 3, ·)\) |
| \(\chi_{ 56 }(9, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 3, ·)\) | \(\chi_{ 56 } ( 27, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 19, ·)\) |
| \(\chi_{ 56 }(27, ·)\) | \(\chi_{ 56 } ( 27, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 3, ·)\) | \(\chi_{ 56 } ( 19, ·)\) | \(\chi_{ 56 } ( 1, ·)\) |