Apt for questions related to Mathieu groups. All the sporadic Mathieu groups are multiply transitive.
Multiply transitive permutation groups: For a natural number $k$, a permutation group $G$ acting on $n$ points is $k$-transitive if, given two sets of points $a_1, ... a_k$ and $b_1, ... b_k$ with the property that all the $a_i$ are distinct and all the $b_i$ are distinct, there is a group element $g$ in $G$ which maps $a_i$ to $b_i$ for each $i$ between $1$ and $k$. Such a group is called sharply $k$-transitive if the element $g$ is unique (i.e. the action on $k$-tuples is regular, rather than just transitive).
The five Mathieu groups $M_(11), M_(12), M_(22), M_(23), and M_(24)$ were the first sporadic groups discovered. They are multiply transitive permutation groups on $11, 12, 22, 23$ or $24$ objects.