Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{6} - x^{5} + 280 x^{4} - 187 x^{3} + 26985 x^{2} - 8836 x + 893759 \)
| $\times$ | \(\chi_{ 2653 } ( 1, ·)\) | \(\chi_{ 2653 } ( 1136, ·)\) | \(\chi_{ 2653 } ( 1138, ·)\) | \(\chi_{ 2653 } ( 757, ·)\) | \(\chi_{ 2653 } ( 1894, ·)\) | \(\chi_{ 2653 } ( 380, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 2653 }(1, ·)\) | \(\chi_{ 2653 } ( 1, ·)\) | \(\chi_{ 2653 } ( 1136, ·)\) | \(\chi_{ 2653 } ( 1138, ·)\) | \(\chi_{ 2653 } ( 757, ·)\) | \(\chi_{ 2653 } ( 1894, ·)\) | \(\chi_{ 2653 } ( 380, ·)\) |
| \(\chi_{ 2653 }(1136, ·)\) | \(\chi_{ 2653 } ( 1136, ·)\) | \(\chi_{ 2653 } ( 1138, ·)\) | \(\chi_{ 2653 } ( 757, ·)\) | \(\chi_{ 2653 } ( 380, ·)\) | \(\chi_{ 2653 } ( 1, ·)\) | \(\chi_{ 2653 } ( 1894, ·)\) |
| \(\chi_{ 2653 }(1138, ·)\) | \(\chi_{ 2653 } ( 1138, ·)\) | \(\chi_{ 2653 } ( 757, ·)\) | \(\chi_{ 2653 } ( 380, ·)\) | \(\chi_{ 2653 } ( 1894, ·)\) | \(\chi_{ 2653 } ( 1136, ·)\) | \(\chi_{ 2653 } ( 1, ·)\) |
| \(\chi_{ 2653 }(757, ·)\) | \(\chi_{ 2653 } ( 757, ·)\) | \(\chi_{ 2653 } ( 380, ·)\) | \(\chi_{ 2653 } ( 1894, ·)\) | \(\chi_{ 2653 } ( 1, ·)\) | \(\chi_{ 2653 } ( 1138, ·)\) | \(\chi_{ 2653 } ( 1136, ·)\) |
| \(\chi_{ 2653 }(1894, ·)\) | \(\chi_{ 2653 } ( 1894, ·)\) | \(\chi_{ 2653 } ( 1, ·)\) | \(\chi_{ 2653 } ( 1136, ·)\) | \(\chi_{ 2653 } ( 1138, ·)\) | \(\chi_{ 2653 } ( 380, ·)\) | \(\chi_{ 2653 } ( 757, ·)\) |
| \(\chi_{ 2653 }(380, ·)\) | \(\chi_{ 2653 } ( 380, ·)\) | \(\chi_{ 2653 } ( 1894, ·)\) | \(\chi_{ 2653 } ( 1, ·)\) | \(\chi_{ 2653 } ( 1136, ·)\) | \(\chi_{ 2653 } ( 757, ·)\) | \(\chi_{ 2653 } ( 1138, ·)\) |