Here is a question which I came up with.

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Let $\displaystyle \mathcal{G}$ be afinite non-abelian group. What are all the possible cardinalities of this group?

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For example, it cannot be 1 because that is the trivial group which is abelian. It cannot be 2 or 3, because up to isomorphism there is only 1 namely $\displaystyle \mathbb{Z}_{2,3}$ which is abelian. With 4 you have two possibilities the usual $\displaystyle \mathbb{Z}_4$ and the Klein 4 group which is also abelian. With 5 (prime) there can only be $\displaystyle \mathbb{Z}_5$. Now with 6 we finally have our first non-abelian group, the dihedral group. With 7 since it is prime we have the same thing ...

Which orders are possible?