Structural taxonomy and complex irreducible representations of non-abelian groups of order p^4

Let p be an odd prime and let G be a non-abelian group of order p⁴. The classification of groups of order p⁴ provides a natural setting for studying the structure of their complex group algebras. In this paper, we consider a non-abelian group G of order p⁴ and determine the primitive central idempotents of the complex group algebra CG. Using these idempotents, we obtain the corresponding decomposition of CG into simple components and describe the irreducible representations of G. The results provide an explicit description of the representation-theoretic structure of the chosen non-abelian group of order p⁴ and illustrate the role of primitive central idempotents in the Wedderburn decomposition of its complex group algebra.