looking for an algebraic descrption of the non-trivial extension of ZxZ by Z2 [closed]

I feel a little silly asking this but am having trouble constructing the non-trivial extension of ZxZ by Z2.

I figure with this example in hand similar examples - e.g. the extension of fundamental group of the Klein bottle by Z2 will be easy.

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@marc: Start by constructing a nontrivial central extension $0\to Z\to Z\to Z_2\to 0$... – Misha Nov 6 at 21:36
Do you mean nontrivial as in nonsplit (nontrivial in cohomology)? This is the torsion-free case, and the answer is easy (Misha's comment is a very good hint). – Steve D Nov 6 at 23:15
Your question would be more appropriate at math.stackexchange.com or one of the other sites listed in the FAQ. – S. Carnahan Nov 7 at 2:37