Automorphism group of symmetric groups - sci.math

Message from discussion Automorphism group of symmetric groups

Al2009

More options Nov 3 2009, 9:05 pm

Newsgroups: sci.math

From: Al2009 <algebra_whate...@yahoo.ca>

Date: Tue, 03 Nov 2009 16:05:06 EST

Local: Tues, Nov 3 2009 9:05 pm

Subject: Automorphism group of symmetric groups

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Hi,

I am trying to understand some automorphism groups of symmetric groups.

It says that

Aut(S_2) = C_2,
Aut(S_6) = S_6 \semidirect C_2
Aut(S_n) = S_n, for n>7.

I know that
G/Z(G) = Inn(G), Out(G) = Aut(G)/Inn(G).

But I can't figure out why Aut(S_6) = S_6 \semidirect C_2
Aut(S_n) = S_n, for n>7.

Any thoughts?

Thanks.

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