Irreducible Representations of Groups of Order 8

Irreducible representations of a group provide the ways for labelling or- bitals, 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, C2xC4 and C2xC2xC2 are obtained using Burnside method and Great Orthogonality Theorem method. Then, comparisons of the two methods are made.