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February 14th, 2018, 04:40 AM   #1
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Group order quick question

today my lecturer wrote:

let G be a subgrup such that $G\in S_{4}$. Then |G|=24

How did he he know it was 24 straight away? Thanks.
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February 14th, 2018, 05:41 AM   #2
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You mean a subgroup of $S_4$? Those don't need to have order $24$ at all...

Maybe he means $|S_4| = 24$. This is because in general, $|S_n| = n!$. This is a combinatorial argument.
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