Irreducible Representations of Groups of Order 8

Abstract

Irreducible representations of a group provide the ways for labelling orbitals, determining molecular orbitals formation and determining vibrational motions for a molecule. A set of irreducible representations represents the ways a particular bond, atom or sets of atoms may respond to a given set of symmetry operations. In this paper, the irreducible representations of all groups of order 8, namely $D_4$, $Q$, $C_8$, $C_2 \times C_4$ and $C_2 \times C_2 \times C_2$ are obtained using Burnside method and Great Orthogonality Theorem method. Then, comparisons of the two methods are made. Keywords: Irreducible representation; group; Burnside method; Great Orthogonality Theorem method.