Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{6} - x^{5} + 154x^{4} - 103x^{3} + 8379x^{2} - 2704x + 160271 \)
| $\times$ | \(\chi_{ 1477 } ( 1, ·)\) | \(\chi_{ 1477 } ( 212, ·)\) | \(\chi_{ 1477 } ( 421, ·)\) | \(\chi_{ 1477 } ( 632, ·)\) | \(\chi_{ 1477 } ( 634, ·)\) | \(\chi_{ 1477 } ( 1054, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 1477 }(1, ·)\) | \(\chi_{ 1477 } ( 1, ·)\) | \(\chi_{ 1477 } ( 212, ·)\) | \(\chi_{ 1477 } ( 421, ·)\) | \(\chi_{ 1477 } ( 632, ·)\) | \(\chi_{ 1477 } ( 634, ·)\) | \(\chi_{ 1477 } ( 1054, ·)\) |
| \(\chi_{ 1477 }(212, ·)\) | \(\chi_{ 1477 } ( 212, ·)\) | \(\chi_{ 1477 } ( 634, ·)\) | \(\chi_{ 1477 } ( 632, ·)\) | \(\chi_{ 1477 } ( 1054, ·)\) | \(\chi_{ 1477 } ( 1, ·)\) | \(\chi_{ 1477 } ( 421, ·)\) |
| \(\chi_{ 1477 }(421, ·)\) | \(\chi_{ 1477 } ( 421, ·)\) | \(\chi_{ 1477 } ( 632, ·)\) | \(\chi_{ 1477 } ( 1, ·)\) | \(\chi_{ 1477 } ( 212, ·)\) | \(\chi_{ 1477 } ( 1054, ·)\) | \(\chi_{ 1477 } ( 634, ·)\) |
| \(\chi_{ 1477 }(632, ·)\) | \(\chi_{ 1477 } ( 632, ·)\) | \(\chi_{ 1477 } ( 1054, ·)\) | \(\chi_{ 1477 } ( 212, ·)\) | \(\chi_{ 1477 } ( 634, ·)\) | \(\chi_{ 1477 } ( 421, ·)\) | \(\chi_{ 1477 } ( 1, ·)\) |
| \(\chi_{ 1477 }(634, ·)\) | \(\chi_{ 1477 } ( 634, ·)\) | \(\chi_{ 1477 } ( 1, ·)\) | \(\chi_{ 1477 } ( 1054, ·)\) | \(\chi_{ 1477 } ( 421, ·)\) | \(\chi_{ 1477 } ( 212, ·)\) | \(\chi_{ 1477 } ( 632, ·)\) |
| \(\chi_{ 1477 }(1054, ·)\) | \(\chi_{ 1477 } ( 1054, ·)\) | \(\chi_{ 1477 } ( 421, ·)\) | \(\chi_{ 1477 } ( 634, ·)\) | \(\chi_{ 1477 } ( 1, ·)\) | \(\chi_{ 1477 } ( 632, ·)\) | \(\chi_{ 1477 } ( 212, ·)\) |