# Central extension

From Groupprops

## Definition

A **central extension** is a group extension where the base normal subgroup is a central subgroup, i.e., it is contained in the center of the whole group.

Central extensions are significant because the central extensions for a given normal subgroup (in this case central subgroup) and quotient group are classified by the second cohomology group for trivial group action of the quotient group on the normal subgroup.