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Number of supersolvable groups of order n.
2

%I #6 Oct 30 2022 18:19:59

%S 1,1,1,2,1,2,1,5,2,2,1,4,1,2,1,14,1,5,1,5,2,2,1,12,2,2,5,4,1,4,1,51,1,

%T 2,1,11,1,2,2,14,1,6,1,4,2,2,1,42,2,5,1,5,1,15,2,12,2,2,1,11,1,2,4,

%U 267,1,4,1,5,1,4,1,37,1,2,2,4,1,6,1,51

%N Number of supersolvable groups of order n.

%C A finite group is supersolvable if it has a normal series with cyclic factors. Huppert showed that a finite group is supersolvable iff the index of any maximal subgroup is prime.

%H B. Huppert, <a href="https://eudml.org/doc/169349">Über das Produkt von paarweise vertauschbaren zyklischen Gruppen</a>, Math. Z. 58 (1954).

%Y Cf. A000001, A066085.

%K nonn,nice

%O 1,4

%A _Reiner Martin_, Dec 29 2001