The transitivity of a permutation group $G$ is the largest non-negative integer $k$ for which $G$ is $k$-transitive. In other words, the transitivity of $G$ is $k$ if $G$ is $k$-transitive, but not $\left(k+1\right)$-transitive. (By convention, the transitivity of an intransitive group is equal to $0$.)

The Transitivity( G ) command returns the transitivity of the permutation group G. The group G must be an instance of a permutation group.

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

$\mathrm{Transitivity}\left(\mathrm{Alt}\left(4\right)\right)$

$2$

$\mathrm{Transitivity}\left(\mathrm{Symm}\left(4\right)\right)$

$4$

$\mathrm{Transitivity}\left(\mathrm{Alt}\left(5\right)\right)$

$3$

$\mathrm{Transitivity}\left(\mathrm{Symm}\left(5\right)\right)$

$5$

$\mathrm{Transitivity}\left(\mathrm{MathieuGroup}\left(23\right)\right)$

$4$

The GroupTheory[Transitivity] command was introduced in Maple 2016.

For more information on Maple 2016 changes, see Updates in Maple 2016.