Schoenflies notation

Because a point group alone is completely adequate to describe the symmetry of a molecule, the notation is often sufficient and commonly used for spectroscopy.

A vertical mirror plane (containing the principal axis) is denoted σv; a horizontal mirror plane (perpendicular to the principal axis) is denoted σh.

In three dimensions, there are an infinite number of point groups, but all of them can be classified by several families.

All groups that do not contain more than one higher-order axis (order 3 or more) can be arranged as shown in a table below; symbols in red are rarely used.

While in case of point groups, Schönflies symbol defines the symmetry elements of group unambiguously, the additional superscript for space group doesn't have any information about translational symmetry of space group (lattice centering, translational components of axes and planes), hence one needs to refer to special tables, containing information about correspondence between Schönflies and Hermann–Mauguin notation.