How are point group character tables typeset correctly?

Notations and conventions used for the description of symmetry in rigid molecules are established in Notations and conventions in molecular spectroscopy: Part 2. Symmetry notation (IUPAC Recommendations 1997):

Symbols for symmetry operators are printed italic, with sub- and super-scripts that are upright except for the variables $k$ and $n$ which are replaced by numbers for a specific operator.

For example:
$E$ – identity operator
$\sigma$ – reflection operator for reflection across a general plane
$\sigma_\mathrm{h}$ – reflection operator for reflection across a horizontal plane
$\sigma_\mathrm{v}$ – reflection operator for reflection across a vertical plane
$C_n{}^k$ – $n$-fold rotation operator for $k$ successive rotations through an angle of $2\pi/n$ about an $n$-fold rotation axis, where $n = 2, 3, \ldots$; $k = 1, 2, \ldots, (n-1)$
$S_n{}^k$ – $n$-fold rotation-reflection operator for $k$ successive rotation-reflections about an $n$-fold rotation-reflection axis for a rotation through an angle of $2\pi/n$ followed by a reflection in a plane perpendicular to the axis, where $n = 2, 3, \ldots$; $k = 1, 2, \ldots, (n-1)$
$i$ – inversion operator through the centre of symmetry

Likewise,

Symbols for symmetry groups are printed italic with upright subscripts, following common usage.

For example:
$C_n$, $S_{2n}$, $D_n$, $D_{n\mathrm{h}}$, $D_{n\mathrm{d}}$, $C_{n\mathrm{v}}$, $C_{n\mathrm{h}}$, $T$, $T_\mathrm{h}$, $T_\mathrm{d}$, $O$, $O_\mathrm{h}$, $I_\mathrm{h}$, $C_{\infty\mathrm{v}}$, $D_{\infty\mathrm{h}}$

However,

Symbols for irreducible representations of point groups, which are usually called symmetry species in spectroscopy, are printed upright.

For example:
$\mathrm{A}$, $\mathrm{B}$, $\mathrm{E}$, $\mathrm{A}_1$, $\mathrm{A}_2$

The example table given in the question should thus be typeset as follows: