Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} - x^{3} - 54x^{2} - 136x - 64 \)
| $\times$ | \(\chi_{ 145 } ( 1, ·)\) | \(\chi_{ 145 } ( 128, ·)\) | \(\chi_{ 145 } ( 144, ·)\) | \(\chi_{ 145 } ( 17, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 145 }(1, ·)\) | \(\chi_{ 145 } ( 1, ·)\) | \(\chi_{ 145 } ( 128, ·)\) | \(\chi_{ 145 } ( 144, ·)\) | \(\chi_{ 145 } ( 17, ·)\) |
| \(\chi_{ 145 }(128, ·)\) | \(\chi_{ 145 } ( 128, ·)\) | \(\chi_{ 145 } ( 144, ·)\) | \(\chi_{ 145 } ( 17, ·)\) | \(\chi_{ 145 } ( 1, ·)\) |
| \(\chi_{ 145 }(144, ·)\) | \(\chi_{ 145 } ( 144, ·)\) | \(\chi_{ 145 } ( 17, ·)\) | \(\chi_{ 145 } ( 1, ·)\) | \(\chi_{ 145 } ( 128, ·)\) |
| \(\chi_{ 145 }(17, ·)\) | \(\chi_{ 145 } ( 17, ·)\) | \(\chi_{ 145 } ( 1, ·)\) | \(\chi_{ 145 } ( 128, ·)\) | \(\chi_{ 145 } ( 144, ·)\) |