Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{6} - 2x^{5} - 12x^{4} + 18x^{3} + 23x^{2} - 16x + 1 \)
| $\times$ | \(\chi_{ 84 } ( 1, ·)\) | \(\chi_{ 84 } ( 37, ·)\) | \(\chi_{ 84 } ( 71, ·)\) | \(\chi_{ 84 } ( 23, ·)\) | \(\chi_{ 84 } ( 25, ·)\) | \(\chi_{ 84 } ( 11, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 84 }(1, ·)\) | \(\chi_{ 84 } ( 1, ·)\) | \(\chi_{ 84 } ( 37, ·)\) | \(\chi_{ 84 } ( 71, ·)\) | \(\chi_{ 84 } ( 23, ·)\) | \(\chi_{ 84 } ( 25, ·)\) | \(\chi_{ 84 } ( 11, ·)\) |
| \(\chi_{ 84 }(37, ·)\) | \(\chi_{ 84 } ( 37, ·)\) | \(\chi_{ 84 } ( 25, ·)\) | \(\chi_{ 84 } ( 23, ·)\) | \(\chi_{ 84 } ( 11, ·)\) | \(\chi_{ 84 } ( 1, ·)\) | \(\chi_{ 84 } ( 71, ·)\) |
| \(\chi_{ 84 }(71, ·)\) | \(\chi_{ 84 } ( 71, ·)\) | \(\chi_{ 84 } ( 23, ·)\) | \(\chi_{ 84 } ( 1, ·)\) | \(\chi_{ 84 } ( 37, ·)\) | \(\chi_{ 84 } ( 11, ·)\) | \(\chi_{ 84 } ( 25, ·)\) |
| \(\chi_{ 84 }(23, ·)\) | \(\chi_{ 84 } ( 23, ·)\) | \(\chi_{ 84 } ( 11, ·)\) | \(\chi_{ 84 } ( 37, ·)\) | \(\chi_{ 84 } ( 25, ·)\) | \(\chi_{ 84 } ( 71, ·)\) | \(\chi_{ 84 } ( 1, ·)\) |
| \(\chi_{ 84 }(25, ·)\) | \(\chi_{ 84 } ( 25, ·)\) | \(\chi_{ 84 } ( 1, ·)\) | \(\chi_{ 84 } ( 11, ·)\) | \(\chi_{ 84 } ( 71, ·)\) | \(\chi_{ 84 } ( 37, ·)\) | \(\chi_{ 84 } ( 23, ·)\) |
| \(\chi_{ 84 }(11, ·)\) | \(\chi_{ 84 } ( 11, ·)\) | \(\chi_{ 84 } ( 71, ·)\) | \(\chi_{ 84 } ( 25, ·)\) | \(\chi_{ 84 } ( 1, ·)\) | \(\chi_{ 84 } ( 23, ·)\) | \(\chi_{ 84 } ( 37, ·)\) |