On the Character Tables of Finite Point Groups

Abstract

A new method for the "complete" construction of the character tables of all the finite point groups is presented. In an explicit way, only the character tables of the five nonisomorphic rotational groups (Cn, Dn, T, O, I) have been derived, because those of the remaining groups can be obtained through isomorphisms and direct products. The characters of the 1-dimensional irreducible representations are calculated using the generators and the defining relations of the groups, while for the multi-dimensional ones explicit formulas are given.