# Finite complete group

From Groupprops

This article defines a property that can be evaluated for finite groups (and hence, a particular kind of group property)

View other properties of finite groups OR View all group properties

## Definition

A **finite complete group** is a finite group that is also a complete group: it satisfies the following two conditions:

- It is a centerless group: its center is trivial.
- It is a group in which every automorphism is inner.

In other words, a finite complete group is a finite group such that the natural map is an isomorphism.