Let $Q$ be a complete product of the permutation group $H$ and an arbitrary finite group $G$ and let $R(Q, K)$ define the group algebra of the group $Q$ over the field of the complex numbers $K$.
We determine the system of the primitive idempotents of the algebra $R(Q, K)$ to which all the irreducible representations of the group $Q$ over the field $K$ correspond.
The necessary and sufficient conditions are also obtained for the equivalency of two irreducible representations of the group $Q$ over the field $K$.
In the case when the group $H$ is cyclic, we give formulas of the number of irreducible representations of fixed degree.
Citation Example:Aisenberg N. N. On representation of the complete product of finite
groups // Ukr. Mat. Zh. - 1961. - 13, № 4. - pp. 5-12.