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wpolly

2008-06-09 07:30

What is this group?

on [URL]http://www.win.tue.nl/~aeb/graphs/Brouwer-Haemers.html[/URL], I see that the automorphism group of a certain graph is described as [tex]3^4:((2\times S_6).2)[/tex].

I understand this group is a composition of [tex]Z_3^4,Z_2\times S_6,Z_2[/tex],but exactly what does the . and : represent? Is it semidirect product, wreath product, or something else? I've been unable to find more informations on this notation elsewhere..

R.D. Silverman

2008-06-09 12:14

[QUOTE=wpolly;135499]on [URL]http://www.win.tue.nl/~aeb/graphs/Brouwer-Haemers.html[/URL], I see that the automorphism group of a certain graph is described as [tex]3^4:((2\times S_6).2)[/tex].

I understand this group is a composition of [tex]Z_3^4,Z_2\times S_6,Z_2[/tex],but exactly what does the . and : represent? Is it semidirect product, wreath product, or something else? I've been unable to find more informations on this notation elsewhere..[/QUOTE]

It appears to be a wreath product.

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