Sharply 3 transitive actions on finite sets

Question

Motivation. if $q=n-1$ is a prime power then the action of Mobius transformations on $X=\mathbf{F}_q\cup\{\infty\}$ is sharply 3 transitive (namely for any distinct $x_1,x_2,x_3\in X$ and any distinct $y_1,y_2,y_3\in X$ there is a unique group element mapping $x_j$ to $y_j$ for $j=1,2,3$).
Question. for which other values of $n$ does there exist a sharply 3 transitive action on a set of $n$ elements.

Answer 1

They are the only $n$ (assuming that you are thinking of finite groups). The finite sharply $2$- and $3$-transitive groups were classified by Zassenhaus in the 1930s.

See here for example for references.