[GAP Forum] Re: Galois group

[Mowsey]

To find the Galois group of x^8-2 in GAP one can use:

x:=Indeterminate(Rationals);
poly:=x^8-2;
g:=TransitiveGroup(Degree(poly), GaloisType(poly));
GeneratorsOfGroup(g);
Elements(g);

This will set g to TransitiveGroup(8,8) = <(1,2,3,4,5,6,7,8),
(1,3)(2,6)(5,7)> which is isomorphic to <a,b : a^2=b^8=1, ab=b^3a>
In Pari/GP galois groups are identifed by their size, but
in GAP they are identified by their degree. In Maple, one can
use "galois(x^8-2);" to get several descriptions of the group,

"8T8", {"[D(4)]2", "2D_8(8)"}, "-", 16, {"(1 2 3 4 5 6 7 8)", "(1 3)(2 6)(5 7)"}