Fixed-class tuple fraction is bounded away from one for groups not of that class
Suppose is a positive integer. Suppose is a finite group that is not a nilpotent group of class at most . In other words, may be a nilpotent group of class strictly greater than or it may be a non-nilpotent group.
Then, the class c tuple fraction of is at most:
Moreover, this bound is tight, because it is attained for any of the three maximal class groups of order (class ) -- see classification of finite 2-groups of maximal class.