Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{6} - x^{5} + 3 x^{4} + 5 x^{2} - 2 x + 1 \)
| $\times$ | \(\chi_{ 21 } ( 1, ·)\) | \(\chi_{ 21 } ( 16, ·)\) | \(\chi_{ 21 } ( 2, ·)\) | \(\chi_{ 21 } ( 4, ·)\) | \(\chi_{ 21 } ( 8, ·)\) | \(\chi_{ 21 } ( 11, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 21 }(1, ·)\) | \(\chi_{ 21 } ( 1, ·)\) | \(\chi_{ 21 } ( 16, ·)\) | \(\chi_{ 21 } ( 2, ·)\) | \(\chi_{ 21 } ( 4, ·)\) | \(\chi_{ 21 } ( 8, ·)\) | \(\chi_{ 21 } ( 11, ·)\) |
| \(\chi_{ 21 }(16, ·)\) | \(\chi_{ 21 } ( 16, ·)\) | \(\chi_{ 21 } ( 4, ·)\) | \(\chi_{ 21 } ( 11, ·)\) | \(\chi_{ 21 } ( 1, ·)\) | \(\chi_{ 21 } ( 2, ·)\) | \(\chi_{ 21 } ( 8, ·)\) |
| \(\chi_{ 21 }(2, ·)\) | \(\chi_{ 21 } ( 2, ·)\) | \(\chi_{ 21 } ( 11, ·)\) | \(\chi_{ 21 } ( 4, ·)\) | \(\chi_{ 21 } ( 8, ·)\) | \(\chi_{ 21 } ( 16, ·)\) | \(\chi_{ 21 } ( 1, ·)\) |
| \(\chi_{ 21 }(4, ·)\) | \(\chi_{ 21 } ( 4, ·)\) | \(\chi_{ 21 } ( 1, ·)\) | \(\chi_{ 21 } ( 8, ·)\) | \(\chi_{ 21 } ( 16, ·)\) | \(\chi_{ 21 } ( 11, ·)\) | \(\chi_{ 21 } ( 2, ·)\) |
| \(\chi_{ 21 }(8, ·)\) | \(\chi_{ 21 } ( 8, ·)\) | \(\chi_{ 21 } ( 2, ·)\) | \(\chi_{ 21 } ( 16, ·)\) | \(\chi_{ 21 } ( 11, ·)\) | \(\chi_{ 21 } ( 1, ·)\) | \(\chi_{ 21 } ( 4, ·)\) |
| \(\chi_{ 21 }(11, ·)\) | \(\chi_{ 21 } ( 11, ·)\) | \(\chi_{ 21 } ( 8, ·)\) | \(\chi_{ 21 } ( 1, ·)\) | \(\chi_{ 21 } ( 2, ·)\) | \(\chi_{ 21 } ( 4, ·)\) | \(\chi_{ 21 } ( 16, ·)\) |