A060249 Size of the automorphism group of the symmetric group S_n.

1, 1, 6, 24, 120, 1440, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000

Offset: 1

Author

Ola Veshta (olaveshta(AT)my-deja.com), Mar 22 2001

Keywords

• nonn
• easy

Comments

For all n except n=2 and n=6, Aut(S_n) is S_n itself, i.e. S_n has no outer automorphisms. Aut(S_2) is trivial and Aut(S_6) is of order 2*|S_6| = 1440 - there is an outer involution.

Crossrefs

Cf. A000142.

Programs

PARI

if(n>6,n!,[1, 1, 6, 24, 120, 1440][n]) \\ Charles R Greathouse IV, Oct 12 2015

Formula

a(n) = n! except for n=2 and 6.

Extensions

Offset corrected by Stephen A. Silver, Feb 09 2013