  In this paper we calculate the character table of a sharply $5$-transitive
subgroup of ${\rm Alt}(12)$, and of a sharply $4$-transitive subgroup of ${\rm
Alt}(11)$. Our presentation of these calculations is new because we make no
reference to the sporadic simple Mathieu groups, and instead deduce the desired
character tables using only the existence of the stated multiply transitive
permutation representations.
