On $\CYRSH$-rigidity of groups of order $p^6$

Abstract

Let $G$ be a group and $Out_c(G)$ be the group of its class-preserving outer automorphisms. We compute $|Out_c(G)|$ for all the group $G$ of order $p^6$, where $p$ is an odd prime. As an application, we observe that if $G$ is a $\CYRSH$-rigid group of order $p^6$, then it's Bogomolov multiplier $B_0(G)$ is zero.