= Direct product of cyclic groups of orders four and two
{title2=$C_4\times C_2=\langle c,a\mid c^4=a^2=e,\ ca=ac\rangle$}
This <abelian group> has eight elements $c^ra^s$, with $r$ taken modulo four and $s$ modulo two. Its <group operation> adds these exponent pairs separately. The elements of order two are $c^2,a,c^2a$, and the other four nonidentity elements $c,c^3,ca,c^3a$ have order four. It is a <direct product of groups> rather than a <cyclic group>, since no element has order eight.
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