  A partial group with $n+1$ elements is, when regarded as a symmetric
simplicial set, of dimension at most $n$. This dimension is $n$ if and only if
the partial group is a group. As a consequence of the first statement, finite
partial groups are genuinely finite, despite being seemingly specified by
infinitely much data. In particular, finite partial groups have only finitely
many im-partial subgroups. We also consider dimension of partial groupoids.
