Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \)
$\times$ | \(\chi_{ 7 } ( 1, ·)\) | \(\chi_{ 7 } ( 2, ·)\) | \(\chi_{ 7 } ( 3, ·)\) | \(\chi_{ 7 } ( 4, ·)\) | \(\chi_{ 7 } ( 5, ·)\) | \(\chi_{ 7 } ( 6, ·)\) |
---|---|---|---|---|---|---|
\(\chi_{ 7 }(1, ·)\) | \(\chi_{ 7 } ( 1, ·)\) | \(\chi_{ 7 } ( 2, ·)\) | \(\chi_{ 7 } ( 3, ·)\) | \(\chi_{ 7 } ( 4, ·)\) | \(\chi_{ 7 } ( 5, ·)\) | \(\chi_{ 7 } ( 6, ·)\) |
\(\chi_{ 7 }(2, ·)\) | \(\chi_{ 7 } ( 2, ·)\) | \(\chi_{ 7 } ( 4, ·)\) | \(\chi_{ 7 } ( 6, ·)\) | \(\chi_{ 7 } ( 1, ·)\) | \(\chi_{ 7 } ( 3, ·)\) | \(\chi_{ 7 } ( 5, ·)\) |
\(\chi_{ 7 }(3, ·)\) | \(\chi_{ 7 } ( 3, ·)\) | \(\chi_{ 7 } ( 6, ·)\) | \(\chi_{ 7 } ( 2, ·)\) | \(\chi_{ 7 } ( 5, ·)\) | \(\chi_{ 7 } ( 1, ·)\) | \(\chi_{ 7 } ( 4, ·)\) |
\(\chi_{ 7 }(4, ·)\) | \(\chi_{ 7 } ( 4, ·)\) | \(\chi_{ 7 } ( 1, ·)\) | \(\chi_{ 7 } ( 5, ·)\) | \(\chi_{ 7 } ( 2, ·)\) | \(\chi_{ 7 } ( 6, ·)\) | \(\chi_{ 7 } ( 3, ·)\) |
\(\chi_{ 7 }(5, ·)\) | \(\chi_{ 7 } ( 5, ·)\) | \(\chi_{ 7 } ( 3, ·)\) | \(\chi_{ 7 } ( 1, ·)\) | \(\chi_{ 7 } ( 6, ·)\) | \(\chi_{ 7 } ( 4, ·)\) | \(\chi_{ 7 } ( 2, ·)\) |
\(\chi_{ 7 }(6, ·)\) | \(\chi_{ 7 } ( 6, ·)\) | \(\chi_{ 7 } ( 5, ·)\) | \(\chi_{ 7 } ( 4, ·)\) | \(\chi_{ 7 } ( 3, ·)\) | \(\chi_{ 7 } ( 2, ·)\) | \(\chi_{ 7 } ( 1, ·)\) |