Suppose is a finite group, is the complex field. If we want to find all irreducible modules, a method is to decompose the regular module into a direct sum. This way is not difficult to realize if the order of the group is small, however, the calculation is much complicated when the orders of groups are large. For any natural number , let the group be a cycle group or a dihedral group , a decomposition of direct sum of irreducible modules of the regular module, and the isomorphic relationship among the irreducible modules are given in this paper. Our method is as follows. To get a decomposition of direct sum of irreducible modules of the regular module, we first construct all irreducible modules satisfying the condition of direct sum, then the isomorphic relationship among the irreducible modules is obtained by module representation theory.
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