A symmetry element can have more than one symmetry operation associated with it.

The symmetry operations can be represented in many ways.

Any symmetry operation in a molecule's point group acting on the molecule itself will leave it unchanged.

If there are symmetry operations relating equivalent groups, two other factors have to be considered.

Each of the five symmetry elements has a symmetry operation.

A set of symmetry operations form a group when:

The order of a group is the number of symmetry operations for that group.

Physical properties and wave functions must be invariant with respect to symmetry operations.

This means that for every pair of flags there is a symmetry operation mapping the first flag to the second.

On the other hand, if the molecule has some symmetry operations, then further ordering is possible.