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I have seen the page demonstrating that it is practically impossible to classify all nilpotent groups, but could you classify all groups of maximal nilpotency class?

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    What is that "maximal nilpotency class"??2012-06-27
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    @DonAntonio: A group of order $p^n$ will have class at most $n-1$; a $p$-group is said to be "of maximal class" if its order is $p^n$ and the class is *exactly* $n-1$. The $p$-groups of maximal class were essentially described by Blackburn, and the Coclass Conjecture programme (now theorems) was based on attempting to emulate his ideas for more general $p$-groups.2012-06-27
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    @Arturo: Provided $n\ge 2$.2012-06-27

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