# Name this property: First symmetric group in which a given group appears

For all finite groups $G$, define $S(G)$ to be the smallest $n\in\mathbb{Z}^+$ such that there exists an $H\leq S_n$ isomorphic to $G$ — i.e., $S(G)$ is the index of the first symmetric group in which $G$ can be embedded. Is there a standard (or at least somewhat common) name or notation for $S(G)$ or a similar concept?

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«Minimal degree of a faithful permutation representation» – Mariano Suárez-Alvarez May 23 '12 at 19:53
@MarianoSuárez-Alvarez: Why not make that an answer? – jwodder May 23 '12 at 20:14