A378280 Number of subgroups of S_n isomorphic to S_4, where S_n is the n-th symmetric group.

0, 0, 0, 1, 5, 60, 560, 5740, 58716, 734160, 8337120, 133212420, 1769490580

Offset: 1

Author

Jianing Song, Nov 21 2024

Keywords

• nonn
• hard
• more

Crossrefs

Column k=4 of A378163.

Cf. A000085, A378279, A378281.

Programs

GAP

A378280 := function(n)
local S;
S := SymmetricGroup(n);
return Sum(IsomorphicSubgroups(S, SymmetricGroup(4)), x->Index(S, Normalizer(S, Image(x))));
end; # See A378163