Two important method of finding the irreducible representations of group were considered, the Burnside method and the Great Orthogonality Theorem. The irreducible representations of cyclic group of order 8 () and the dihedral group () of the same order were obtain using the two methods, and the result were compared. Both method can be used to find the irreducible representations of and respectively. The Burnside method is lengthy and can be applied to any group, while in the case of the Great Orthogonality Theorem method the groups type need to be identified first.
