A proper rotation refers to simple rotation about an axis. Such operations are denoted by  where  is a rotation of  or  performed  times. The superscript  is omitted if it is equal to one.  is a rotation through 360°, where . It is equivalent to the Identity () operation.  is a rotation of 180°, as   is a rotation of 120°, as  and so on. 
Here the molecule can be rotated into equivalent positions around an axis. An example of a molecule with  symmetry is the water () molecule. If the  molecule is rotated by 180° about an axis passing through the oxygen atom, no detectable difference before and after the  operation is observed. 
Order  of an axis can be regarded as a number of times that, for the least rotation which gives an equivalent configuration, that rotation must be repeated to give a configuration identical to the original structure (i.e. a 360° or 2 rotation). An example of this is  proper rotation, which rotates by   represents the first rotation around the  axis by   is the rotation by  while  is the rotation by   is the identical configuration because it gives the original structure, and it is called an identity element (). Therefore,  is an order of three, and is often referred to as a threefold axis.