The degree of a permutation group is the cardinality of the set upon which it acts.  Since permutation groups act on sets of the form $\left\{1\,2\,\dots \,n\right\}$, the degree is the positive integer $n$.

The Degree( G ) command returns the degree of a permutation group G.

Some group constructors, such as those for the symmetric and alternating groups take a degree parameter as input, and the Degree command returns this value.

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

$G≔\mathrm{Group}\left(\mathrm{Perm}\left(\left[\left[1\,2\right]\right]\right)\,\mathrm{Perm}\left(\left[\left[2\,3\,4\right]\right]\right)\right)$

$G≔⟨\left(1\,2\right)\,\left(2\,3\,4\right)⟩$

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

$4$

$\mathrm{Degree}\left(\mathrm{DihedralGroup}\left(14\right)\right)$

$14$

$\mathrm{Degree}\left(\mathrm{AlternatingGroup}\left(10\right)\right)$

$10$

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

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