mersenneforum.org (https://www.mersenneforum.org/index.php)
-   Math (https://www.mersenneforum.org/forumdisplay.php?f=8)
-   -   What is this group? (https://www.mersenneforum.org/showthread.php?t=10380)

 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 $$3^4:((2\times S_6).2)$$.

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=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 $$3^4:((2\times S_6).2)$$.

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..[/QUOTE]

It appears to be a wreath product.

 All times are UTC. The time now is 11:10.