So I was working through some problems in a book on $p$-groups and noticed that $p$-groups have some really nice properties. So I started computing what the values of $|G/Z(G)|$ for $p$-groups. I decided to see what it would be and found that it cannot attain the value of $p$. I am interested in the whethere $|G/Z(G)|$ can attain all other powers of $p$?
In general I am interesting in the values that $|G/Z(G)|$ can achieve.
Any help is greatly appreciated.