Given a finite nonabelian semisimple group $G$, we describe those groups that have the same holomorph as $G$, that is, those regular subgroups $N\simeq G$ of $S(G)$, the group of permutations on the set $G$, such that $N_{S(G)}(N)=N_{S(G)}(\rho(G))$, where $\rho$ is the right regular representation of $G$.

中文翻译：

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关于有限半单群的全纯

给定一个有限的非阿贝尔半单群 $G$，我们描述那些与 $G$ 具有相同全形的群，即 $S(G)$ 的那些正则子群 $N\simeq G$，在设置 $G$，使得 $N_{S(G)}(N)=N_{S(G)}(\rho(G))$，其中 $\rho$ 是 $G$ 的正确正则表示。