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a) Determine the smallest symmetric group $S_n$ that contains a subgroup isomorphic to H, generated by $x^4=y^3=1$, $xy=y^2x$.

b) Find a subgroup of $SL_2(F_5)$ that is isomorphic to that group.

My first step was to say that $n$ is at least 4 so that $S_n$ contains an element of order 4. But I tried $S_4$ and it didn't quite work. After that I couldn't make much progress.

Any help appreciated.

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    @DerekHolt Oh righttt why didn't I think of that. Thank you! Any hint on the subgroup of $SL_2(F_5)$?2012-11-13

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