A378279 Number of subgroups of S_n isomorphic to S_3, where S_n is the n-th symmetric group.

0, 0, 1, 4, 20, 160, 910, 5936, 53424, 397440, 3304620, 35023120, 322852816

Offset: 1

Author

Jianing Song, Nov 21 2024

Keywords

• nonn
• hard
• more

Crossrefs

Column k=3 of A378163.

Cf. A000085, A378280, A378281, A281097.

Programs

GAP

A378279 := function(n)
local S;
S := SymmetricGroup(n);
return Sum(IsomorphicSubgroups(S, SymmetricGroup(3)), x->Index(S, Normalizer(S, Image(x))));
end;

Formula

a(n) = (A281097(n) - A000085(n))/6. See A378163 for more information.