Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{6} \) \(\mathstrut -\mathstrut x^{5} \) \(\mathstrut +\mathstrut 11 x^{4} \) \(\mathstrut -\mathstrut 6 x^{3} \) \(\mathstrut +\mathstrut 108 x^{2} \) \(\mathstrut -\mathstrut 80 x \) \(\mathstrut +\mathstrut 64 \)
| $\times$ | \(\chi_{ 93 } ( 1, ·)\) | \(\chi_{ 93 } ( 32, ·)\) | \(\chi_{ 93 } ( 67, ·)\) | \(\chi_{ 93 } ( 5, ·)\) | \(\chi_{ 93 } ( 56, ·)\) | \(\chi_{ 93 } ( 25, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 93 }(1, ·)\) | \(\chi_{ 93 } ( 1, ·)\) | \(\chi_{ 93 } ( 32, ·)\) | \(\chi_{ 93 } ( 67, ·)\) | \(\chi_{ 93 } ( 5, ·)\) | \(\chi_{ 93 } ( 56, ·)\) | \(\chi_{ 93 } ( 25, ·)\) |
| \(\chi_{ 93 }(32, ·)\) | \(\chi_{ 93 } ( 32, ·)\) | \(\chi_{ 93 } ( 1, ·)\) | \(\chi_{ 93 } ( 5, ·)\) | \(\chi_{ 93 } ( 67, ·)\) | \(\chi_{ 93 } ( 25, ·)\) | \(\chi_{ 93 } ( 56, ·)\) |
| \(\chi_{ 93 }(67, ·)\) | \(\chi_{ 93 } ( 67, ·)\) | \(\chi_{ 93 } ( 5, ·)\) | \(\chi_{ 93 } ( 25, ·)\) | \(\chi_{ 93 } ( 56, ·)\) | \(\chi_{ 93 } ( 32, ·)\) | \(\chi_{ 93 } ( 1, ·)\) |
| \(\chi_{ 93 }(5, ·)\) | \(\chi_{ 93 } ( 5, ·)\) | \(\chi_{ 93 } ( 67, ·)\) | \(\chi_{ 93 } ( 56, ·)\) | \(\chi_{ 93 } ( 25, ·)\) | \(\chi_{ 93 } ( 1, ·)\) | \(\chi_{ 93 } ( 32, ·)\) |
| \(\chi_{ 93 }(56, ·)\) | \(\chi_{ 93 } ( 56, ·)\) | \(\chi_{ 93 } ( 25, ·)\) | \(\chi_{ 93 } ( 32, ·)\) | \(\chi_{ 93 } ( 1, ·)\) | \(\chi_{ 93 } ( 67, ·)\) | \(\chi_{ 93 } ( 5, ·)\) |
| \(\chi_{ 93 }(25, ·)\) | \(\chi_{ 93 } ( 25, ·)\) | \(\chi_{ 93 } ( 56, ·)\) | \(\chi_{ 93 } ( 1, ·)\) | \(\chi_{ 93 } ( 32, ·)\) | \(\chi_{ 93 } ( 5, ·)\) | \(\chi_{ 93 } ( 67, ·)\) |