Odd-order class two group

Definition
An odd-order class two group is defined in the following equivalent ways:


 * 1) It is an odd-order group that is also a defining ingredient::nilpotent group of class at most two.
 * 2) It is a finite group that is also a Baer Lie group.
 * 3) It is a finite nilpotent group, hence an internal direct product of its Sylow subgroups, each of which has class at most two.