  It is well known that not every finite group arises as the full automorphism
group of some group. Here we show that the situation is dramatically different
when considering the category of partial groups, ${{\mathcal P}art}$, as
defined by Chermak: given any group $H$ there exists infinitely many non
isomorphic partial groups ${\mathbb M}$ such that
$\operatorname{Aut}_{{\mathcal P}art}({\mathbb M})\cong H$. To prove this
result, given any simple undirected graph $G$ we construct a partial group
${\mathbb P}(G)$, called the path partial group associated to $G$, such that
$\operatorname{Aut}_{{\mathcal P}art}\big({\mathbb P}(G)\big)\cong
\operatorname{Aut}_{{\mathcal G}raphs}(G)$. As a consequence, we solve the Kahn
realizability problem in the category of simplicial sets.
