Point symmetry groups and operators revisited

We have studied finite point symmetry group (PSG) operators. Hermitian and unitary properties of these operators were deduced by analyzing their matrix representations. We showed that PSG operators: E, C-2, sigma and S-2, and PSG groups: C-1, C-i, C-2, C-s, D-2, C-2v, C-2h and D-2h are the only unitary and hermitian ones. The algebraic relationships between point symmetry groups are analyzed on the basis of isomorphism, homomorphism and descent-of-symmetry. Hasse diagram for homomorphic PSG is derived for the first time.