The only subgroup of $S_{10}$ with the same number of elements as $G$ which I can recall is $S_4$. Is this the subgroup?

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# Find subgroup of $S_{10}$ isomorphic to $G=mathbb{Z}/4mathbb{Z}times mathbb{Z}/6mathbb{Z}$

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The only subgroup of $S_{10}$ with the same number of elements as $G$ which I can recall is $S_4$. Is this the subgroup?

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