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For a finite group G, we denote by $\mu(G)$, and c(G), the minimal degree offaithful permutation representation of G, and the minimal degree of faithfulrepresentation of G by quasi-permutation matrices over the complex field C,respectively. In this article, we study $\mu(G)$, and c(G) for various classesof finite non-abelian p-groups with cyclic center. We prove a result fornormally monomial p-groups with cyclic center which generalizes a result ofBehravesh for finite p-groups of nilpotency class 2 with cyclic center [5,Theorem 4.12]. We also compute minimal degrees for some classes of metabelianp-groups.

Minimal Faithful Quasi-Permutation Representation Degree of p-Groups with Cyclic Center