Motivated by some characterizations of the hypercenter of a finite group, we investigate in every group G, with respect to any subgroup closed group class its -preserver - a canonical characteristic subgroup, which coincides with the hypercenter of G when is the class of nilpotent groups and G is finite. We study general properties of discuss special properties and show the utility of the introduced concepts in the case of concrete classes.

canonical characteristic subgroups, hypercenter, nilpotency, FC-groups, local properties.