What is this group?

wpolly · 2008-06-09, 07:30

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

I understand this group is a composition of $Z_3^4,Z_2\times S_6,Z_2$ ,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:

Originally Posted by wpolly

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

I understand this group is a composition of $Z_3^4,Z_2\times S_6,Z_2$ ,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..

It appears to be a wreath product.

2008-06-09, 07:30	#1
wpolly Sep 2002 Vienna, Austria 11011011₂ Posts	What is this group? on http://www.win.tue.nl/~aeb/graphs/Brouwer-Haemers.html, I see that the automorphism group of a certain graph is described as $3^4:((2\times S_6).2)$ . I understand this group is a composition of $Z_3^4,Z_2\times S_6,Z_2$ ,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.. Last fiddled with by wpolly on 2008-06-09 at 07:54

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