Groups

Let G be a finite group. A group element h is said to be conujugate to the group element k, h ˜ k, if there exists a g ∈ G such that k = ghg⁻¹. For G the number of conjugacy classes is equal to the number of irreducible matrix representations. In a character table the rows correspond to irreducible group representations and columns to classes of group elements. If the irreducible matrix representation is given by an n × n matrix (n ≥ 2) then the trace of this square matrix is the element in the table…