Irreducible Representations of Groups of Order 8

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 D4, Q, C8, C2 × C4 and C2 × C2 × C2 are obtained using Burnside method and Great Orthogonality Theorem method. Then, comparisons of the two methods are made.