Character table of G6n
= Character table of G6n
{c}
{title2=$G_{6n}$}
The conjugacy classes of $G_{6n}$ are
$$
C_r=\{a^{2r}\},\qquad
D_r=\{a^{2r}b,a^{2r}b^2\},\qquad
E_r=\{a^{2r+1},a^{2r+1}b,a^{2r+1}b^2\},
$$
for $0\leq r<n$. With $0\leq j<2n$ and $0\leq k<n$, the linear character $\lambda_j$ and two-dimensional character $\chi_k$ have values
$$
\begin{array}{c|ccc}
&C_r&D_r&E_r\\ \hline
\lambda_j&\xi^{2jr}&\xi^{2jr}&\xi^{j(2r+1)}\\
\chi_k&2\xi^{2kr}&-\xi^{2kr}&0.
\end{array}
$$