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 S n where n is the order. Since the improper rotation is the combination of a proper rotation and a reflection, S n will always exist whenever C n and a perpendicular plane exist separately. S 1 is usually denoted as σ, a reflection operation about a mirror plane. S 2 is usually denoted as i, an inversion operation about an inversion center. When n is an even number S n n = E , but when n is odd S n 2 n = E .