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## Cyclic groups and isomorphisms

I have a question where it says prove that $G \cong C_3 \times C_5$ when G has order 15.

And I assumed that as 3 and 5 are co-prime then $C_{15} \cong C_3 \times C_5$, which would mean that $G \cong C_{15}$?

So every group of order 15 is isomorohic to a cyclic group of order 15?

Doesn't seem right?

Help would be appreciated! Thanks!

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