Molecular symmetry
For example, water (H2O) which has the C2v symmetry described above.  The 2px orbital of oxygen is oriented perpendicular to the plane of the molecule and switches sign with a C2 and a σv'(yz) operation, but remains unchanged with the other two operations (obviously, the character for the identity operation is always +1). This orbital's character set is thus {1, -1, 1, -1}, corresponding to the B1 irreducible representation. Similarly, the 2pz orbital is seen to have the symmetry of the A1 irreducible representation, 2py B2, and the  3d''xy orbital A2. These assignments and others are in the rightmost two columns of the table.