\begin{definition}[Definition:Characteristic Subgroup]
Let $G$ be a group.
Let $H$ be a subgroup such that:
:$\forall \phi \in \Aut G: \phi \sqbrk H = H$
where $\Aut G$ is the automorphism group of $G$.
Then $H$ is  '''characteristic (in $G$)''', or '''a characteristic subgroup of $G$'''.
\end{definition}