An Example on Computing the Irreducible Representation of Finite Metacyclic Groups by Using Great Orthogonality Theorem Method

Representation theory is a study of real realizations of the axiomatic systems of abstract algebra. for any group, the number of possible representative sets of matrices is infinite, but they can all be reduced to a single fundamental set, called the irreducible representations of the group. this paper focuses on an example of finite metacyclic groups of class two of order 16. the irreducible representation of that group is found by using great orthogonality theorem method.