Group theory: finding a molecule's point group

$E$ (identity), $C_n$ (rotation by $2\pi/n$), $\sigma$ (reflection), $i$ (inversion), $S_n$ (improper rotation: $C_n$ then $\sigma_h$). The principal axis is the $C_n$ axis of highest order. A plane is $\sigma_h$ if it is perpendicular to it, $\sigma_v$ if it contains it, $\sigma_d$ if it contains it while bisecting two $C_2$ axes.