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

$K$ is the global number field defined by \( x^{4} - 12 x^{2} + 25 \)

$\times$ \(\chi_{ 88 } ( 1, ·)\) \(\chi_{ 88 } ( 43, ·)\) \(\chi_{ 88 } ( 45, ·)\) \(\chi_{ 88 } ( 87, ·)\)
\(\chi_{ 88 }(1, ·)\) \(\chi_{ 88 } ( 1, ·)\) \(\chi_{ 88 } ( 43, ·)\) \(\chi_{ 88 } ( 45, ·)\) \(\chi_{ 88 } ( 87, ·)\)
\(\chi_{ 88 }(43, ·)\) \(\chi_{ 88 } ( 43, ·)\) \(\chi_{ 88 } ( 1, ·)\) \(\chi_{ 88 } ( 87, ·)\) \(\chi_{ 88 } ( 45, ·)\)
\(\chi_{ 88 }(45, ·)\) \(\chi_{ 88 } ( 45, ·)\) \(\chi_{ 88 } ( 87, ·)\) \(\chi_{ 88 } ( 1, ·)\) \(\chi_{ 88 } ( 43, ·)\)
\(\chi_{ 88 }(87, ·)\) \(\chi_{ 88 } ( 87, ·)\) \(\chi_{ 88 } ( 45, ·)\) \(\chi_{ 88 } ( 43, ·)\) \(\chi_{ 88 } ( 1, ·)\)