SymmetricGroup, AlternatingGroup, DihedralGroup and many other named groups are built-in symbols.
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}}]}]
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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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QUICK REFERENCE: Group Theory »