An improper rotation involves two operation steps: a proper rotation followed by reflection through a plane perpendicular to the rotation axis. The improper rotation is represented by the symbol  where  is the order. Since the improper rotation is the combination of a proper rotation and a reflection,  will always exist whenever  and a perpendicular plane exist separately.  is usually denoted as , a reflection operation about a mirror plane.  is usually denoted as , an inversion operation about an inversion center. When  is an even number  but when  is odd 
Rotation axes, mirror planes and inversion centres are  symmetry elements, not symmetry operations. The rotation axis of the highest order is known as the principal rotation axis. It is conventional to set the Cartesian -axis of the molecule to contain the principal rotation axis.