The GaloisGroup command returns the Galois group of a polynomial p over the field $\mathbb{Q}$ of rational numbers, or over the rational function field, $\mathbb{Q}\left(t_1\,t_1\,\dots \,t_k\right)$ as a permutation group.  Since the polynomial p is required to be irreducible, the resulting permutation group is transitive.

The degree of p may be at most 9 in the univariate case, and at most 8 in the multivariate case.

$\mathrm{with}\left(\mathrm{GroupTheory}\right)\:$

$G≔\mathrm{GaloisGroup}\left(x^5-x+1\,x\right)$

$G≔\mathrm{Gal}\left(x^5-x+1\,x\right)$

$\mathrm{GroupOrder}\left(G\right)$

$120$

$\mathrm{IsTransitive}\left(G\right)$

$\mathrm{true}$

The GroupTheory[GaloisGroup] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.