  The average order of a finite group G is denoted by o(G). In this note, we
classify groups whose average orders are less than o(S4), where S4 is the
symmetric group on four elements. Moreover, we prove that G \cong S4 if and
only if o(G) = o(S4). As a consequence of our results we give a
characterization for some finite groups by the average order. In [9, Theorem
1.2], the groups whose average orders are less than o(A4) are classified. It is
worth mentioning that to get our results we avoid using the main theorems of
[9] and our results leads to reprove those theorems.
