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$\begingroup$

Well my queston is the title exactly. Im trying to get an isomorphism between a 5-sylow subgroup of alternating group $A_{20}$ and something familiar. But I don't know where to start. I know that $A_{20}$ is simple so I can't have a unique 5-sylow correct? and its order must be $5^{4}$.

Any help is appreciated. Thanks

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    I should also say you are exactly correct: it cannot have a unique Sylow 5-subgroup, in fact it has 633568231296 of them. The order of every single one of them is $5^4 = \color{red}{5}\cdot \color{purple}{5}\cdot\color{green}{5} \cdot \color{blue}{5}$.2011-11-03
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    Im sorry I dont understand this. Why does P look like this, and how does that make it isomorphic to C_{4} x C_{4} x C_{4} x C_{4}?2011-11-03

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