We calculate the character table of a sharply 5-transitive subgroup of \alter(12)‎, ‎and of a sharply 4-transitive subgroup of \alter(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.