Character Tables Of Some Finite Groups Of Lower Orders

It is a classic and important subject to study the structures of finite groups by representation theory of finite groups,such as Frobenius's theorem and p~aq~b-theorem.According to the character tables of finite groups,we can determine whether the Solvable Groups,whether the Nilpotent Groups,and both have the same characteristics that are the subject of such isomorphism.Thus,from the group's character table,we can get a large number of group theory on the information.Constructing the character tables of finite groups of lower orders is a highly professional problem.Many studies did not specifically discuss this issue,and there is no general way for constructing the character tables.In this thesis,we study the character tables of some finite groups of lower orders(more than 30 and less than 51).First,we study the isomorphism sorts of finite groups of lower orders by isomorphic classifications of finite groups.Then,we construct the character tables of finite groups of lower orders because isomorphic groups have the same character table.