Irreducible Representations of Some Finite Groups

In this thesis we compute the irreducible representations and the characters of some certain finite groups. We first provide the necessary overview on linear algebra, group theory and the representations theory. Then, we compute the irreducible representations of finite cyclic groups, smaller symmetric groups and the direct products of the two groups. Finally, we give a general method to compute the irreducible representations of 𝑆����𝑛���� by using Young diagrams and provide the Frobenius formula to obtain the characters for these irreducible representations. Keywords: Representation, Character, Cyclic groups, Symmetric groups, Young diagram, Frobenius formula.