Group Theory

Get a list of group elements:

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GroupElements[SymmetricGroup[2]]

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Determine the generators of a group:

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GroupGenerators[SymmetricGroup[3]]

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Create a permutation group from two generators:

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PermutationGroup[{Cycles[{{3, 1, 2}}], Cycles[{{2, 5, 6}}]}]

Compute its order:

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GroupOrder[%]

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Show the multiplication table for a group:

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TableForm[GroupMultiplicationTable[DihedralGroup[2]], 
 TableHeadings -> Automatic]

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Visualize it with a Cayley graph:

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CayleyGraph[DihedralGroup[2]]

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