Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{6} + 6x^{4} + 9x^{2} + 1 \)
| $\times$ | \(\chi_{ 36 } ( 1, ·)\) | \(\chi_{ 36 } ( 19, ·)\) | \(\chi_{ 36 } ( 7, ·)\) | \(\chi_{ 36 } ( 25, ·)\) | \(\chi_{ 36 } ( 13, ·)\) | \(\chi_{ 36 } ( 31, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 36 }(1, ·)\) | \(\chi_{ 36 } ( 1, ·)\) | \(\chi_{ 36 } ( 19, ·)\) | \(\chi_{ 36 } ( 7, ·)\) | \(\chi_{ 36 } ( 25, ·)\) | \(\chi_{ 36 } ( 13, ·)\) | \(\chi_{ 36 } ( 31, ·)\) |
| \(\chi_{ 36 }(19, ·)\) | \(\chi_{ 36 } ( 19, ·)\) | \(\chi_{ 36 } ( 1, ·)\) | \(\chi_{ 36 } ( 25, ·)\) | \(\chi_{ 36 } ( 7, ·)\) | \(\chi_{ 36 } ( 31, ·)\) | \(\chi_{ 36 } ( 13, ·)\) |
| \(\chi_{ 36 }(7, ·)\) | \(\chi_{ 36 } ( 7, ·)\) | \(\chi_{ 36 } ( 25, ·)\) | \(\chi_{ 36 } ( 13, ·)\) | \(\chi_{ 36 } ( 31, ·)\) | \(\chi_{ 36 } ( 19, ·)\) | \(\chi_{ 36 } ( 1, ·)\) |
| \(\chi_{ 36 }(25, ·)\) | \(\chi_{ 36 } ( 25, ·)\) | \(\chi_{ 36 } ( 7, ·)\) | \(\chi_{ 36 } ( 31, ·)\) | \(\chi_{ 36 } ( 13, ·)\) | \(\chi_{ 36 } ( 1, ·)\) | \(\chi_{ 36 } ( 19, ·)\) |
| \(\chi_{ 36 }(13, ·)\) | \(\chi_{ 36 } ( 13, ·)\) | \(\chi_{ 36 } ( 31, ·)\) | \(\chi_{ 36 } ( 19, ·)\) | \(\chi_{ 36 } ( 1, ·)\) | \(\chi_{ 36 } ( 25, ·)\) | \(\chi_{ 36 } ( 7, ·)\) |
| \(\chi_{ 36 }(31, ·)\) | \(\chi_{ 36 } ( 31, ·)\) | \(\chi_{ 36 } ( 13, ·)\) | \(\chi_{ 36 } ( 1, ·)\) | \(\chi_{ 36 } ( 19, ·)\) | \(\chi_{ 36 } ( 7, ·)\) | \(\chi_{ 36 } ( 25, ·)\) |