

A060249


Size of the automorphism group of the symmetric group S_n.


3



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

1,3


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.


LINKS

Table of n, a(n) for n=1..20.


FORMULA

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


PROG

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


CROSSREFS

Cf. A000142.
Sequence in context: A182083 A293049 A293123 * A052557 A188232 A274072
Adjacent sequences: A060246 A060247 A060248 * A060250 A060251 A060252


KEYWORD

nonn,easy


AUTHOR

Ola Veshta (olaveshta(AT)mydeja.com), Mar 22 2001


EXTENSIONS

Offset corrected by Stephen A. Silver, Feb 09 2013


STATUS

approved



