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Is there any Mathematica command or well known technique to take the direct product between two symmetric/permutation groups?

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    $\begingroup$ can you give example? $\endgroup$ Jun 25 '14 at 5:10
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PG = PermutationGroup[{Cycles[{{1, 3}, {2, 4}}], Cycles[{{1, 5}, {4, 6}}]}];

PermutationProduct @@ GroupElements @ PG

Cycles[{{1, 5}, {4, 6}}]

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