I only know $2$-groups of nilpotency class $2$ and order less than or equal to $32$, and wondering if there are finite $2$-groups of order $>32$ and nilpotency class $2$? Your suggestions are appreciated. Thanks.
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Yes, there are $2$-groups of any order (which is a power of $2$ and at least $8$) and nilpotency class $2$. It is easy enough to construct examples via semidirect products of abelian $2$-groups. – Tobias Kildetoft Jun 11 '15 at 11:35
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@ Tobias, can you give an example of such construction please? – Chuks Jun 11 '15 at 11:39
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Actually, sorry, that was the wrong way to get examples. Just take direct product of class $2$ ones with abelian ones. – Tobias Kildetoft Jun 11 '15 at 11:44
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@ Tobias, many thanks. I now feel cool! – Chuks Jun 11 '15 at 11:53
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Search the list of groups of order $64$ here for nilpotency class $2$. Therer are already many examples. – Dietrich Burde Jun 11 '15 at 13:05