The size of a minimal generating set for primitive $\frac{3}{2}$-transitive groups

We refer to $d(G)$ as the minimal size of a generating set of a finite group $G$, and say that $G$ is $d$-generated if $d(G)\leq d$. A transitive permutation group $G$ is called $\frac{3}{2}$-transitive if the point stabilizer $G_\alpha$ is nontrivial and its orbits distinct from $\{\alpha\}$ are of the same size. We prove that $d(G)\leq4$ for every primitive $\frac{3}{2}$-transitive permutation group $G$ and, moreover, $G$ is $2$-generated except for the rather particular solvable affine groups that we describe completely. In particular, all finite $2$-transitive and $2$-homogeneous groups are $2$-generated. We also show that every finite group whose abelian subgroups are cyclic is $2$-generated, and so is every Frobenius complement.