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February 14th, 2018, 04:40 AM  #1 
Senior Member Joined: Jan 2016 From: Blackpool Posts: 104 Thanks: 2  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. 
February 14th, 2018, 05:41 AM  #2 
Senior Member Joined: Oct 2009 Posts: 884 Thanks: 340 
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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