Paper 3, Section I, D

What does it mean to say that groups $G$ and $H$ are isomorphic?

Prove that no two of $C_{8}, C_{4} \times C_{2}$ and $C_{2} \times C_{2} \times C_{2}$ are isomorphic. [Here $C_{n}$ denotes the cyclic group of order $n$.]

Give, with justification, a group of order 8 that is not isomorphic to any of those three groups.

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