The GetIsomorphism( 'm1', 'm2' ) command returns an isomorphism, in the form of a permutation of 1..n, where m1 and m2 are of order n, which effects an isomorphism from m1 to m2.  In case m1 and m2 are not isomorphic, then the value false is returned.

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

$\mathrm{m1}≔⟨⟨⟨1\left|2\right|3⟩\,⟨2\left|3\right|1⟩\,⟨3\left|1\right|2⟩⟩⟩$

$\mathrm{m1}≔\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 1\\ 3& 1& 2\end{array}\right]$

$\mathrm{m2}≔⟨⟨⟨2\left|3\right|1⟩\,⟨3\left|1\right|2⟩\,⟨1\left|2\right|3⟩⟩⟩$

$\mathrm{m2}≔\left[\begin{array}{ccc}2& 3& 1\\ 3& 1& 2\\ 1& 2& 3\end{array}\right]$

$\mathrm{GetIsomorphism}\left(\mathrm{m1}\,\mathrm{m2}\right)$

$\left[3\,1\,2\right]$

$\mathrm{m3}≔⟨⟨⟨1\left|2\right|1⟩\,⟨2\left|3\right|2⟩\,⟨3\left|1\right|3⟩⟩⟩$

$\mathrm{m3}≔\left[\begin{array}{ccc}1& 2& 1\\ 2& 3& 2\\ 3& 1& 3\end{array}\right]$

$\mathrm{GetIsomorphism}\left(\mathrm{m1}\,\mathrm{m3}\right)$

$\mathrm{false}$

The Magma[GetIsomorphism] command was introduced in Maple 15.

For more information on Maple 15 changes, see Updates in Maple 15.