  For any group $G$ and set $A$, consider the shift action of $G$ on the full
shift $A^G$. A configuration $x \in A^G$ has \emph{least period} $H \leq G$ if
the stabiliser of $x$ is precisely $H$. Among other things, the number of such
configurations is interesting as it provides an upper bound for the size of the
corresponding $\text{Aut}(A^G)$-orbit. In this paper we show that if $G$ is
finitely generated and $H$ is of finite index, then the number of
configurations in $A^G$ with least period $H$ may be computed using the
M\"obius function of the lattice of subgroups of finite index in $G$. Moreover,
when $H$ is a normal subgroup, we classify all situations such that the number
of $G$-orbits with least period $H$ is at most $10$.
