A284210 Number of subgroups of order n of the symmetric group Sym(n) on n symbols.

1, 1, 1, 7, 6, 280, 120, 25335, 11200, 276696, 362880, 374838255, 39916800, 2414617920, 11721790080

Offset: 1

Author

Jens Voß, Mar 23 2017

Keywords

• nonn
• more

Comments

The diagonal of A243748. - R. J. Mathar, Mar 30 2017 [edited by Peter Munn, Mar 06 2025]

Examples

			The group Sym(4) contains 3 cyclic groups of order 4, 3 non-normal elementary abelian groups of order 4 and one normal group of order 4, so A284210(4) = 3 + 3 + 1 = 7.
		

Programs

GAP

List([1..14], n -> Sum(List(Filtered(ConjugacyClassesSubgroups(SymmetricGroup(n)), c -> Size(Representative(c)) = n)), c -> Size(c)));

Formula

If n is prime, A284210(n) = (n-2)!.