Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{6} - 12x^{4} + 36x^{2} - 8 \)
| $\times$ | \(\chi_{ 72 } ( 1, ·)\) | \(\chi_{ 72 } ( 37, ·)\) | \(\chi_{ 72 } ( 49, ·)\) | \(\chi_{ 72 } ( 25, ·)\) | \(\chi_{ 72 } ( 13, ·)\) | \(\chi_{ 72 } ( 61, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 72 }(1, ·)\) | \(\chi_{ 72 } ( 1, ·)\) | \(\chi_{ 72 } ( 37, ·)\) | \(\chi_{ 72 } ( 49, ·)\) | \(\chi_{ 72 } ( 25, ·)\) | \(\chi_{ 72 } ( 13, ·)\) | \(\chi_{ 72 } ( 61, ·)\) |
| \(\chi_{ 72 }(37, ·)\) | \(\chi_{ 72 } ( 37, ·)\) | \(\chi_{ 72 } ( 1, ·)\) | \(\chi_{ 72 } ( 13, ·)\) | \(\chi_{ 72 } ( 61, ·)\) | \(\chi_{ 72 } ( 49, ·)\) | \(\chi_{ 72 } ( 25, ·)\) |
| \(\chi_{ 72 }(49, ·)\) | \(\chi_{ 72 } ( 49, ·)\) | \(\chi_{ 72 } ( 13, ·)\) | \(\chi_{ 72 } ( 25, ·)\) | \(\chi_{ 72 } ( 1, ·)\) | \(\chi_{ 72 } ( 61, ·)\) | \(\chi_{ 72 } ( 37, ·)\) |
| \(\chi_{ 72 }(25, ·)\) | \(\chi_{ 72 } ( 25, ·)\) | \(\chi_{ 72 } ( 61, ·)\) | \(\chi_{ 72 } ( 1, ·)\) | \(\chi_{ 72 } ( 49, ·)\) | \(\chi_{ 72 } ( 37, ·)\) | \(\chi_{ 72 } ( 13, ·)\) |
| \(\chi_{ 72 }(13, ·)\) | \(\chi_{ 72 } ( 13, ·)\) | \(\chi_{ 72 } ( 49, ·)\) | \(\chi_{ 72 } ( 61, ·)\) | \(\chi_{ 72 } ( 37, ·)\) | \(\chi_{ 72 } ( 25, ·)\) | \(\chi_{ 72 } ( 1, ·)\) |
| \(\chi_{ 72 }(61, ·)\) | \(\chi_{ 72 } ( 61, ·)\) | \(\chi_{ 72 } ( 25, ·)\) | \(\chi_{ 72 } ( 37, ·)\) | \(\chi_{ 72 } ( 13, ·)\) | \(\chi_{ 72 } ( 1, ·)\) | \(\chi_{ 72 } ( 49, ·)\) |