Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 \)
| $\times$ | \(\chi_{ 28 } ( 1, ·)\) | \(\chi_{ 28 } ( 3, ·)\) | \(\chi_{ 28 } ( 5, ·)\) | \(\chi_{ 28 } ( 9, ·)\) | \(\chi_{ 28 } ( 11, ·)\) | \(\chi_{ 28 } ( 13, ·)\) | \(\chi_{ 28 } ( 15, ·)\) | \(\chi_{ 28 } ( 17, ·)\) | \(\chi_{ 28 } ( 19, ·)\) | \(\chi_{ 28 } ( 23, ·)\) | \(\chi_{ 28 } ( 25, ·)\) | \(\chi_{ 28 } ( 27, ·)\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{ 28 }(1, ·)\) | \(\chi_{ 28 } ( 1, ·)\) | \(\chi_{ 28 } ( 3, ·)\) | \(\chi_{ 28 } ( 5, ·)\) | \(\chi_{ 28 } ( 9, ·)\) | \(\chi_{ 28 } ( 11, ·)\) | \(\chi_{ 28 } ( 13, ·)\) | \(\chi_{ 28 } ( 15, ·)\) | \(\chi_{ 28 } ( 17, ·)\) | \(\chi_{ 28 } ( 19, ·)\) | \(\chi_{ 28 } ( 23, ·)\) | \(\chi_{ 28 } ( 25, ·)\) | \(\chi_{ 28 } ( 27, ·)\) |
| \(\chi_{ 28 }(3, ·)\) | \(\chi_{ 28 } ( 3, ·)\) | \(\chi_{ 28 } ( 9, ·)\) | \(\chi_{ 28 } ( 15, ·)\) | \(\chi_{ 28 } ( 27, ·)\) | \(\chi_{ 28 } ( 5, ·)\) | \(\chi_{ 28 } ( 11, ·)\) | \(\chi_{ 28 } ( 17, ·)\) | \(\chi_{ 28 } ( 23, ·)\) | \(\chi_{ 28 } ( 1, ·)\) | \(\chi_{ 28 } ( 13, ·)\) | \(\chi_{ 28 } ( 19, ·)\) | \(\chi_{ 28 } ( 25, ·)\) |
| \(\chi_{ 28 }(5, ·)\) | \(\chi_{ 28 } ( 5, ·)\) | \(\chi_{ 28 } ( 15, ·)\) | \(\chi_{ 28 } ( 25, ·)\) | \(\chi_{ 28 } ( 17, ·)\) | \(\chi_{ 28 } ( 27, ·)\) | \(\chi_{ 28 } ( 9, ·)\) | \(\chi_{ 28 } ( 19, ·)\) | \(\chi_{ 28 } ( 1, ·)\) | \(\chi_{ 28 } ( 11, ·)\) | \(\chi_{ 28 } ( 3, ·)\) | \(\chi_{ 28 } ( 13, ·)\) | \(\chi_{ 28 } ( 23, ·)\) |
| \(\chi_{ 28 }(9, ·)\) | \(\chi_{ 28 } ( 9, ·)\) | \(\chi_{ 28 } ( 27, ·)\) | \(\chi_{ 28 } ( 17, ·)\) | \(\chi_{ 28 } ( 25, ·)\) | \(\chi_{ 28 } ( 15, ·)\) | \(\chi_{ 28 } ( 5, ·)\) | \(\chi_{ 28 } ( 23, ·)\) | \(\chi_{ 28 } ( 13, ·)\) | \(\chi_{ 28 } ( 3, ·)\) | \(\chi_{ 28 } ( 11, ·)\) | \(\chi_{ 28 } ( 1, ·)\) | \(\chi_{ 28 } ( 19, ·)\) |
| \(\chi_{ 28 }(11, ·)\) | \(\chi_{ 28 } ( 11, ·)\) | \(\chi_{ 28 } ( 5, ·)\) | \(\chi_{ 28 } ( 27, ·)\) | \(\chi_{ 28 } ( 15, ·)\) | \(\chi_{ 28 } ( 9, ·)\) | \(\chi_{ 28 } ( 3, ·)\) | \(\chi_{ 28 } ( 25, ·)\) | \(\chi_{ 28 } ( 19, ·)\) | \(\chi_{ 28 } ( 13, ·)\) | \(\chi_{ 28 } ( 1, ·)\) | \(\chi_{ 28 } ( 23, ·)\) | \(\chi_{ 28 } ( 17, ·)\) |
| \(\chi_{ 28 }(13, ·)\) | \(\chi_{ 28 } ( 13, ·)\) | \(\chi_{ 28 } ( 11, ·)\) | \(\chi_{ 28 } ( 9, ·)\) | \(\chi_{ 28 } ( 5, ·)\) | \(\chi_{ 28 } ( 3, ·)\) | \(\chi_{ 28 } ( 1, ·)\) | \(\chi_{ 28 } ( 27, ·)\) | \(\chi_{ 28 } ( 25, ·)\) | \(\chi_{ 28 } ( 23, ·)\) | \(\chi_{ 28 } ( 19, ·)\) | \(\chi_{ 28 } ( 17, ·)\) | \(\chi_{ 28 } ( 15, ·)\) |
| \(\chi_{ 28 }(15, ·)\) | \(\chi_{ 28 } ( 15, ·)\) | \(\chi_{ 28 } ( 17, ·)\) | \(\chi_{ 28 } ( 19, ·)\) | \(\chi_{ 28 } ( 23, ·)\) | \(\chi_{ 28 } ( 25, ·)\) | \(\chi_{ 28 } ( 27, ·)\) | \(\chi_{ 28 } ( 1, ·)\) | \(\chi_{ 28 } ( 3, ·)\) | \(\chi_{ 28 } ( 5, ·)\) | \(\chi_{ 28 } ( 9, ·)\) | \(\chi_{ 28 } ( 11, ·)\) | \(\chi_{ 28 } ( 13, ·)\) |
| \(\chi_{ 28 }(17, ·)\) | \(\chi_{ 28 } ( 17, ·)\) | \(\chi_{ 28 } ( 23, ·)\) | \(\chi_{ 28 } ( 1, ·)\) | \(\chi_{ 28 } ( 13, ·)\) | \(\chi_{ 28 } ( 19, ·)\) | \(\chi_{ 28 } ( 25, ·)\) | \(\chi_{ 28 } ( 3, ·)\) | \(\chi_{ 28 } ( 9, ·)\) | \(\chi_{ 28 } ( 15, ·)\) | \(\chi_{ 28 } ( 27, ·)\) | \(\chi_{ 28 } ( 5, ·)\) | \(\chi_{ 28 } ( 11, ·)\) |
| \(\chi_{ 28 }(19, ·)\) | \(\chi_{ 28 } ( 19, ·)\) | \(\chi_{ 28 } ( 1, ·)\) | \(\chi_{ 28 } ( 11, ·)\) | \(\chi_{ 28 } ( 3, ·)\) | \(\chi_{ 28 } ( 13, ·)\) | \(\chi_{ 28 } ( 23, ·)\) | \(\chi_{ 28 } ( 5, ·)\) | \(\chi_{ 28 } ( 15, ·)\) | \(\chi_{ 28 } ( 25, ·)\) | \(\chi_{ 28 } ( 17, ·)\) | \(\chi_{ 28 } ( 27, ·)\) | \(\chi_{ 28 } ( 9, ·)\) |
| \(\chi_{ 28 }(23, ·)\) | \(\chi_{ 28 } ( 23, ·)\) | \(\chi_{ 28 } ( 13, ·)\) | \(\chi_{ 28 } ( 3, ·)\) | \(\chi_{ 28 } ( 11, ·)\) | \(\chi_{ 28 } ( 1, ·)\) | \(\chi_{ 28 } ( 19, ·)\) | \(\chi_{ 28 } ( 9, ·)\) | \(\chi_{ 28 } ( 27, ·)\) | \(\chi_{ 28 } ( 17, ·)\) | \(\chi_{ 28 } ( 25, ·)\) | \(\chi_{ 28 } ( 15, ·)\) | \(\chi_{ 28 } ( 5, ·)\) |
| \(\chi_{ 28 }(25, ·)\) | \(\chi_{ 28 } ( 25, ·)\) | \(\chi_{ 28 } ( 19, ·)\) | \(\chi_{ 28 } ( 13, ·)\) | \(\chi_{ 28 } ( 1, ·)\) | \(\chi_{ 28 } ( 23, ·)\) | \(\chi_{ 28 } ( 17, ·)\) | \(\chi_{ 28 } ( 11, ·)\) | \(\chi_{ 28 } ( 5, ·)\) | \(\chi_{ 28 } ( 27, ·)\) | \(\chi_{ 28 } ( 15, ·)\) | \(\chi_{ 28 } ( 9, ·)\) | \(\chi_{ 28 } ( 3, ·)\) |
| \(\chi_{ 28 }(27, ·)\) | \(\chi_{ 28 } ( 27, ·)\) | \(\chi_{ 28 } ( 25, ·)\) | \(\chi_{ 28 } ( 23, ·)\) | \(\chi_{ 28 } ( 19, ·)\) | \(\chi_{ 28 } ( 17, ·)\) | \(\chi_{ 28 } ( 15, ·)\) | \(\chi_{ 28 } ( 13, ·)\) | \(\chi_{ 28 } ( 11, ·)\) | \(\chi_{ 28 } ( 9, ·)\) | \(\chi_{ 28 } ( 5, ·)\) | \(\chi_{ 28 } ( 3, ·)\) | \(\chi_{ 28 } ( 1, ·)\) |