On the order of the commutator subgroup and the Schur multiplier of a finite \(p\)-group (Q1180646)

Let \(G\) be a finite \(p\)-group. By a result of \textit{J. Wiegold} [Math. Z. 89, 345--347 (1965; Zbl 0134.03002)] if \(| G/Z(G)|=p^n\) and \(| G'|=p^t\), then \(t\le n(n-1)/2\). In this note the author shows that if equality holds then either \(G/Z(G)\) is an elementary abelian group or it is an extraspecial group. \{Reviewer's remark: It is easy to see that in the extraspecial case \(G/Z(G)\) must have order \(p^3\).\}