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A284210 Number of subgroups of order n of the symmetric group Sym(n) on n symbols. 2
1, 1, 1, 7, 6, 280, 120, 25335, 11200, 276696, 362880, 374838255, 39916800, 2414617920, 11721790080 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The diagonal of A243748 (once the 0's for non-divisors of n are filled in). - R. J. Mathar, Mar 30 2017

LINKS

Table of n, a(n) for n=1..15.

FORMULA

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

EXAMPLE

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.

PROG

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

CROSSREFS

Sequence in context: A249992 A223531 A130553 * A002394 A274210 A105167

Adjacent sequences:  A284207 A284208 A284209 * A284211 A284212 A284213

KEYWORD

nonn,more

AUTHOR

Jens Voß, Mar 23 2017

STATUS

approved

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Last modified May 31 05:50 EDT 2020. Contains 334747 sequences. (Running on oeis4.)