Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{6} + 10 x^{4} + 24 x^{2} + 8 \)
| $\times$ | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 11, ·)\) | \(\chi_{ 56 } ( 51, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 43, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 56 }(1, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 11, ·)\) | \(\chi_{ 56 } ( 51, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 43, ·)\) |
| \(\chi_{ 56 }(11, ·)\) | \(\chi_{ 56 } ( 11, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 51, ·)\) | \(\chi_{ 56 } ( 43, ·)\) | \(\chi_{ 56 } ( 25, ·)\) |
| \(\chi_{ 56 }(51, ·)\) | \(\chi_{ 56 } ( 51, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 43, ·)\) | \(\chi_{ 56 } ( 11, ·)\) | \(\chi_{ 56 } ( 9, ·)\) |
| \(\chi_{ 56 }(25, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 51, ·)\) | \(\chi_{ 56 } ( 43, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 11, ·)\) |
| \(\chi_{ 56 }(9, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 43, ·)\) | \(\chi_{ 56 } ( 11, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 51, ·)\) |
| \(\chi_{ 56 }(43, ·)\) | \(\chi_{ 56 } ( 43, ·)\) | \(\chi_{ 56 } ( 25, ·)\) | \(\chi_{ 56 } ( 9, ·)\) | \(\chi_{ 56 } ( 11, ·)\) | \(\chi_{ 56 } ( 51, ·)\) | \(\chi_{ 56 } ( 1, ·)\) |