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Hi i'm stuck on this homework question:

"Write down the group table for the permutation group $S_3$."

I've found many answers online but I don't understand how they know how to draw the table out and what goes where. i.e. if i then wanted to do $S_4$ how would that be drawn. Any help would be appreciated thanks.

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    Do you mean, the "headings" for the rows and columns (along the top and left sides)? Or what goes in the individual boxes? It might help to try and describe what you *think* happens -- you might be surprised at how right you are. – 2017-02-15

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There is a helpful page by groupprops, saying: "The purpose of this page is to give a detailed description of the construction of the multiplication table of symmetric group $S_3$. I think, this is want you want.