A separating set for a group G with respect to the group CG is a set of simultaneously diagonalisable linear operators fT
1
; :::; Tr
g of C that distinguish the
invariant subspaces of CG with their eigenspaces. In this thesis, we study the
character table of the irreducible representation of the unitary group G and construct the modi ed character table which consists of the eigenvalues that the class
sum of each conjugacy class of G assigns to an irreducible representation of G:
The separating set for G is then obtained by extracting the class sums which is
associated to each irreducible character distinct pair of eigenvalues.