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Topic: Automorphism group of symmetric groups
Replies: 16   Last Post: Nov 4, 2009 2:48 PM

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Al2009

Posts: 11
Registered: 10/30/09
Automorphism group of symmetric groups
Posted: Nov 3, 2009 4:05 PM
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Hi,

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

http://en.wikipedia.org/wiki/Symmetric_group#Automorphism_group

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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