Finite group that is order statistics-equivalent to an abelian group

Definition
A finite group is termed a finite group that is order statistics-equivalent to an abelian group is a finite group that is order statistics-equivalent (i.e., has the same order statistics) to an defining ingredient::abelian group (in particular, a defining ingredient::finite abelian group.

Equivalently, it is a finite nilpotent group each of whose Sylow subgroups is a group of prime power order order statistics-equivalent to an abelian group.