Abstract: This paper introduces a method of constructing all inequivalent irreducible representations of a finite group using induced representations of its invariant subgroups，and applies it to the solution of the character table of the first kind of crystal point groups. This method is systematic and simple，and can be used as a supplement to the method of solving irreducible representation of the point groups in current textbooks.

Key words: induced representation, irreducible representation, invariant subgroup, character