Symmetric group:S4: The symmetric group of degree four (order 24). See also subgroups of S4 and representations of S4.
Baer norm (DEFINITION): The intersection of the normalizers of all subgroups of the group. Contains the center, and is a hereditarily normal subgroup.
Nilpotent implies center is normality-large (FACT): In a nilpotent group, the center intersects every nontrivial normal subgroup nontrivially.
Characteristic versus normal (SURVEY ARTICLE): There are important differences between a characteristic subgroup and a normal subgroup.