Quasirecognition by prime graph of $C_{n}(4) $, where $ n\geq17 $ is odd

Abstract

Let $G$ be a finite group and let $\Gamma(G) $ be the prime graph of $ G$. We assume that $ n\geq 17$ is an odd number. In this paper, we show that if $ \Gamma(G) = \Gamma(C_{n}(4))$, then $ G$ has a unique non-abelian composition factor isomorphic to $C_{n}(4)$. As consequences of our result, $C_{n}(4)$ is quasirecognizable by its spectrum and by prime graph.