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 $p^4$. The classification of groups of order $p^4$ 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 $p^4$ and determine the primitive central idempotents of the complex group algebra $\mathbb{C}G$. Using these idempotents, we obtain the corresponding decomposition of $\mathbb{C}G$ 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 $p^4$ and illustrate the role of primitive central idempotents in the Wedderburn decomposition of its complex group algebra.