A378281 Number of subgroups of S_n isomorphic to S_5, where S_n is the n-th symmetric group.

0, 0, 0, 0, 1, 12, 84, 560, 3276, 79632, 1105104, 16571808, 176344740

Offset: 1

Author

Jianing Song, Nov 21 2024

Keywords

• nonn
• hard
• more

Crossrefs

Column k=5 of A378163.

Cf. A000085, A378279, A378280.

Programs

GAP

A378281 := function(n)
local S;
S := SymmetricGroup(n);
return Sum(IsomorphicSubgroups(S, SymmetricGroup(5)), x->Index(S, Normalizer(S, Image(x))));
end;