## Low-symmetry groups: $C_1$, $C_\mathrm{s}$, $C_\mathrm{i}$

$$\begin{array}{c|c}
\hline
C_1 & E \\ \hline
\mathrm{A} & 1 \\
\hline
\end{array}$$

$\,$

$$\begin{array}{c|cc|cc}
\hline
C_\mathrm{s} (= C_\mathrm{h}) & E & \sigma_\mathrm{h} & &  \\ \hline
\mathrm{A'} & 1 & 1 & x,y, R_z & x^2, y^2, z^2, xy \\
\mathrm{A''} & 1 & -1 & z, R_x, R_y & xz, yz \\
\hline
\end{array}$$

$\,$

$$\begin{array}{c|cc|cc}
\hline
C_\mathrm{i} (= S_2) & E & i & &  \\ \hline
\mathrm{A_g} & 1 & 1 & R_x, R_y, R_z & x^2, y^2, z^2, xy, xz, yz \\
\mathrm{A_u} & 1 & -1 & x,y,z &  \\
\hline
\end{array}$$