List of Almost Simple 2-transitive Group

This table lists the finite $2$-transitive groups with simple socle. Here $q$ is a prime power $q=p^e;n$ and $d$ are positive integers, $n$ being the degree. $N$ is the socle of $G$. The next column gives the index of $N$ in the largest possible $G$, viz., its normalizer in $S_n$. Groups with the same socle may have different degrees of transitivity; the least and greatest such degrees are given. Note that the socle is $2$-transitive in all cases except one, that is $N=\mathrm{PSL}(2,8)$. The final column gives the number of non-isomorphic actions. (For example, for $\mathrm{PSL}(d,q),d>2$, these actions are on the points and hyperplanes of the projective space.)

ref: Permutation groups - 1999 - Cameron.pdf.

Let $G$ be an almost simple $2$-transitive permutation group with socle $G_0$ and point stabilizer $H=G_{\omega }$. Then $G$ is one of the groups listed in Table 1, and $m(G_0)$ is the Schur multiplier of $G_0$.

Remark. ${}^2{B}_2(q)\cong Sz(q)$ and ${}^2{G}_2(q)\cong R_1(q)$.

ref: On finite permutation groups of rank three - 2024 - Huang, Li, Zhu.pdf.