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

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

Doesn't seem right?

Help would be appreciated! Thanks!