The number of distinct element orders in a finite group

For a finite group $G$ let $ω(G)$ denote its spectrum, the set of orders of its elements, and set $η(G)=|ω(G)|$, the number of distinct element orders. The set $ω(G)$ has been studied intensively, but its cardinality has received little systematic attention as an invariant in its own right. We devel