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?
Classification of finite nilpotent groups of maximal class
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group-theory
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0What is that "maximal nilpotency class"?? – 2012-06-27
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1@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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0@Arturo: Provided $n\ge 2$. – 2012-06-27