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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
added statement of some trivialities, just for completeness:
Besides the cyclic group $\mathbb{Z}/4$ of order 4, the Klein group $\mathbb{Z}/2 \times \mathbb{Z}/2$ is the only other group of order 4, up to isomorphism.
In particular the Klein group is not itself a cyclic group, and it is in fact the smallest non-trivial group which is not a cyclic group.
added cross-link with fundamental theorem of finitely generated abelian groups
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