University of KashanMathematics Interdisciplinary Research2538-36393220181201Groups with Two Extreme Character Degrees and their Minimal Faithful Representations1091158826210.22052/mir.2019.186347.1133ENMahtab DelfaniDepartment of Mathematics, Urmia University, Urmia, IranHoushang BehraveshDepartment of Mathematics, Urmia University, Urmia, IranJournal Article20190518for a finite group G, we denote by p(G) the minimal degree of faithful permutation representations of G, and denote by c(G), the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C. In this paper we will assume that, G is a p-group of exponent p and class 2, where p is prime and cd(G) = {1, |G : Z(G)|<sup>1/2</sup>}. Then we will show that c(G)≤ |G : Z(G)|<sup>1/2</sup> c(Z(G)) , p(G) ≤ |G : Z(G)|<sup>1/2</sup>p(Z(G)):https://mir.kashanu.ac.ir/article_88262_bbea5fc48f8ecb778827001fced83bbd.pdf