An improper rotation is the composition of a rotation about an axis, and reflection in a plane perpendicular to that axis. The order in which the rotation and reflection are performed does not matter (that is, these operations commute). Improper rotation is also defined as the composition of a rotation about an axis, and inversion about a point on the axis. These definitions are equivalent because inversion about a point is equivalent to rotation by 180° about any axis, followed by mirroring about a plane perpendicular to that axis. The symmetry elements for improper rotation are the rotation axis, and either the mirror plane, the inversion point, or both. The improper rotation group of order 2 n is denoted S 2 n.