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1. The problem statement, all variables and given/known data

Find all Sylow 3-subgroups of S_4 and demonstrate that they are all conjugate.

2. Relevant equations

3. The attempt at a solution

I found all the Sylow 3-subgroups, but I am having trouble finding the element that conjugates them. For example, how do you find the element conjugates that <(1,2,3)> and <(2,3,4)>? I could just try all the elements, but there are 24, so that is probably a bad idea...

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# Sylow theory

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