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Is there any non-abelian group of order $n=49$? I assume there should be at least one but I cannot find an example.

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    I took the liberty of removing the boldface text... that seems completely unnecessary.2012-02-25

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The only groups of order $49$ are $\mathbb Z_{49}$ and $\mathbb Z_7\times \mathbb Z_7$ since $49$ is a square of a prime number.