The character table of a sharply 5-transitive subgroup of the alternating group of degree 12

In this paper we calculate the character table of a sharply $5$-transitive subgroup of Alt(12), and of a sharply $4$-transitive subgroup of 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.