Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{6} \) \(\mathstrut +\mathstrut 14 x^{4} \) \(\mathstrut +\mathstrut 56 x^{2} \) \(\mathstrut +\mathstrut 56 \)
| $\times$ | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 5, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 45, ·)\) | \(\chi_{ 56 } ( 13, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 56 }(1, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 5, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 45, ·)\) | \(\chi_{ 56 } ( 13, ·)\) |
| \(\chi_{ 56 }(5, ·)\) | \(\chi_{ 56 } ( 5, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 13, ·)\) | \(\chi_{ 56 } ( 45, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 9, ·)\) |
| \(\chi_{ 56 }(25, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 13, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 5, ·)\) | \(\chi_{ 56 } ( 45, ·)\) |
| \(\chi_{ 56 }(9, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 45, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 13, ·)\) | \(\chi_{ 56 } ( 5, ·)\) |
| \(\chi_{ 56 }(45, ·)\) | \(\chi_{ 56 } ( 45, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 5, ·)\) | \(\chi_{ 56 } ( 13, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 25, ·)\) |
| \(\chi_{ 56 }(13, ·)\) | \(\chi_{ 56 } ( 13, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 45, ·)\) | \(\chi_{ 56 } ( 5, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 1, ·)\) |