Class two characteristic subgroup

Definition
A subgroup of a group is termed a class two characteristic subgroup if it is a group of nilpotency class two and is a characteristic subgroup of the whole group.

Note that group of nilpotency class two means group whose nilpotency class at most two, so this includes abelian characteristic subgroups.

Stronger properties

 * Weaker than::Abelian characteristic subgroup
 * Weaker than::Cyclic characteristic subgroup
 * Weaker than::Critical subgroup
 * Weaker than::Aut-abelian characteristic subgroup

Weaker properties

 * Stronger than::Class two normal subgroup
 * Stronger than::Nilpotent characteristic subgroup