Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{6} \) \(\mathstrut -\mathstrut 10 x^{4} \) \(\mathstrut +\mathstrut 24 x^{2} \) \(\mathstrut -\mathstrut 8 \)
| $\times$ | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 37, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 29, ·)\) | \(\chi_{ 56 } ( 53, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 56 }(1, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 37, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 29, ·)\) | \(\chi_{ 56 } ( 53, ·)\) |
| \(\chi_{ 56 }(37, ·)\) | \(\chi_{ 56 } ( 37, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 29, ·)\) | \(\chi_{ 56 } ( 53, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 1, ·)\) |
| \(\chi_{ 56 }(25, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 29, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 53, ·)\) | \(\chi_{ 56 } ( 37, ·)\) |
| \(\chi_{ 56 }(9, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 53, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 37, ·)\) | \(\chi_{ 56 } ( 29, ·)\) |
| \(\chi_{ 56 }(29, ·)\) | \(\chi_{ 56 } ( 29, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 53, ·)\) | \(\chi_{ 56 } ( 37, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 25, ·)\) |
| \(\chi_{ 56 }(53, ·)\) | \(\chi_{ 56 } ( 53, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 37, ·)\) | \(\chi_{ 56 } ( 29, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 9, ·)\) |