Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} - 12x^{2} + 25 \)
| $\times$ | \(\chi_{ 88 } ( 1, ·)\) | \(\chi_{ 88 } ( 43, ·)\) | \(\chi_{ 88 } ( 45, ·)\) | \(\chi_{ 88 } ( 87, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 88 }(1, ·)\) | \(\chi_{ 88 } ( 1, ·)\) | \(\chi_{ 88 } ( 43, ·)\) | \(\chi_{ 88 } ( 45, ·)\) | \(\chi_{ 88 } ( 87, ·)\) |
| \(\chi_{ 88 }(43, ·)\) | \(\chi_{ 88 } ( 43, ·)\) | \(\chi_{ 88 } ( 1, ·)\) | \(\chi_{ 88 } ( 87, ·)\) | \(\chi_{ 88 } ( 45, ·)\) |
| \(\chi_{ 88 }(45, ·)\) | \(\chi_{ 88 } ( 45, ·)\) | \(\chi_{ 88 } ( 87, ·)\) | \(\chi_{ 88 } ( 1, ·)\) | \(\chi_{ 88 } ( 43, ·)\) |
| \(\chi_{ 88 }(87, ·)\) | \(\chi_{ 88 } ( 87, ·)\) | \(\chi_{ 88 } ( 45, ·)\) | \(\chi_{ 88 } ( 43, ·)\) | \(\chi_{ 88 } ( 1, ·)\) |