If $G$ is a finite group, and $n$ is the least positive integer such that $G$ can be embedded in symmetric group $S_n$, then, should $G$ necessarily contain a subgroup of index $n$?
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closed as too localized by Mark Sapir, Ryan Budney, Martin Brandenburg, Bill Johnson, Benjamin Steinberg Jan 17 '12 at 13:09This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question. 


This is not true. The group $S_3 \times S_2$ can be embedded in $S_5$, but not in smaller symmetric groups. 

