Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$

$K$ is the global number field defined by \( x^{7} - 21x^{5} - 21x^{4} + 91x^{3} + 112x^{2} - 84x - 97 \) Copy content Toggle raw display

$\times$ \(\chi_{ 49 } ( 1, ·)\) \(\chi_{ 49 } ( 36, ·)\) \(\chi_{ 49 } ( 22, ·)\) \(\chi_{ 49 } ( 8, ·)\) \(\chi_{ 49 } ( 43, ·)\) \(\chi_{ 49 } ( 29, ·)\) \(\chi_{ 49 } ( 15, ·)\)
\(\chi_{ 49 }(1, ·)\) \(\chi_{ 49 } ( 1, ·)\) \(\chi_{ 49 } ( 36, ·)\) \(\chi_{ 49 } ( 22, ·)\) \(\chi_{ 49 } ( 8, ·)\) \(\chi_{ 49 } ( 43, ·)\) \(\chi_{ 49 } ( 29, ·)\) \(\chi_{ 49 } ( 15, ·)\)
\(\chi_{ 49 }(36, ·)\) \(\chi_{ 49 } ( 36, ·)\) \(\chi_{ 49 } ( 22, ·)\) \(\chi_{ 49 } ( 8, ·)\) \(\chi_{ 49 } ( 43, ·)\) \(\chi_{ 49 } ( 29, ·)\) \(\chi_{ 49 } ( 15, ·)\) \(\chi_{ 49 } ( 1, ·)\)
\(\chi_{ 49 }(22, ·)\) \(\chi_{ 49 } ( 22, ·)\) \(\chi_{ 49 } ( 8, ·)\) \(\chi_{ 49 } ( 43, ·)\) \(\chi_{ 49 } ( 29, ·)\) \(\chi_{ 49 } ( 15, ·)\) \(\chi_{ 49 } ( 1, ·)\) \(\chi_{ 49 } ( 36, ·)\)
\(\chi_{ 49 }(8, ·)\) \(\chi_{ 49 } ( 8, ·)\) \(\chi_{ 49 } ( 43, ·)\) \(\chi_{ 49 } ( 29, ·)\) \(\chi_{ 49 } ( 15, ·)\) \(\chi_{ 49 } ( 1, ·)\) \(\chi_{ 49 } ( 36, ·)\) \(\chi_{ 49 } ( 22, ·)\)
\(\chi_{ 49 }(43, ·)\) \(\chi_{ 49 } ( 43, ·)\) \(\chi_{ 49 } ( 29, ·)\) \(\chi_{ 49 } ( 15, ·)\) \(\chi_{ 49 } ( 1, ·)\) \(\chi_{ 49 } ( 36, ·)\) \(\chi_{ 49 } ( 22, ·)\) \(\chi_{ 49 } ( 8, ·)\)
\(\chi_{ 49 }(29, ·)\) \(\chi_{ 49 } ( 29, ·)\) \(\chi_{ 49 } ( 15, ·)\) \(\chi_{ 49 } ( 1, ·)\) \(\chi_{ 49 } ( 36, ·)\) \(\chi_{ 49 } ( 22, ·)\) \(\chi_{ 49 } ( 8, ·)\) \(\chi_{ 49 } ( 43, ·)\)
\(\chi_{ 49 }(15, ·)\) \(\chi_{ 49 } ( 15, ·)\) \(\chi_{ 49 } ( 1, ·)\) \(\chi_{ 49 } ( 36, ·)\) \(\chi_{ 49 } ( 22, ·)\) \(\chi_{ 49 } ( 8, ·)\) \(\chi_{ 49 } ( 43, ·)\) \(\chi_{ 49 } ( 29, ·)\)