polgalois

[Mathias Lederer <csab2185@uibk.ac.at>]

The output of the command "polgalois(x)" is a three-component-vector [n,
s, k], where k is the number of the group corresponding to a given pair
(n, s). In the user's guide there is a list that explains the meaning of
k for all polynomials up to degree 7. In this case k=1 except in 2
cases.
But when polgalois(x) is applied to a polynomial  e.g. of degree 11, k
can be a much higher number.

My question is: Where can I find a list which tells me the meaning of k
in the general case? In GTM 138 it says that the number of k refers to
standard literature. So which literature is standard?

And second, can't I get any direct information about the action of the
Galois group on the zeros of the polynomial out of the command
"polgalois"?

Mathias Lederer