A322100 - OEIS

%I #7 Nov 27 2018 09:18:16

%S 1,1,1,2,1,4,1,5,2,6,1,17,1,6,4,75,1,23,1,47,5,6,1,213,2,7,20,30,1,79,

%T 1,12033,3,7,4,436,1,5,4,1963,1,84,1,148,41,4,1

%N Number of minimal transitive permutation groups of degree n.

%C A transitive group is minimal provided it has no proper transitive subgroups.

%H Derek Holt and Gordon Royle, <a href="https://arxiv.org/abs/1811.09015">A Census of Small Transitive Groups and Vertex-Transitive Graphs</a>, arXiv:1811.09015 [math.CO], 2018.

%e There are two transitive groups of degree 3, A_3 and S_3, so A002106(3)=2. However, a(3)=1, because A_3 is minimal, but S_3 has proper transitive subgroups A_3 and S_2.

%Y Cf. A002106.

%K nonn,more

%O 1,4

%A _Danny Rorabaugh_, Nov 26 2018