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AlternatingGroup

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Symbolic alternating group A_n of degree n; stays unevaluated and is consumed by GroupOrder/GroupGenerators/GroupElements

AlternatingGroup[n]
AlternatingGroup[10]//GroupOrder → 1814400AlternatingGroup[4]//GroupElements → {Cycles[{}], Cycles[{{2, 3, 4}}], Cycles[{{2, 4, 3}}], Cycles[{{1, 2}, {3, 4}}], Cycles[{{1, 2, 3}}], Cycles[{{1, 2, 4}}], Cycles[{{1, 3, 2}}], Cycles[{{1, 3, 4}}], Cycles[{{1, 3}, {2, 4}}], Cycles[{{1, 4, 2}}], Cycles[{{1, 4, 3}}], Cycles[{{1, 4}, {2, 3}}]}AlternatingGroup[10]//GroupGenerators → {Cycles[{{1, 2, 3}}], Cycles[{{2, 3, 4, 5, 6, 7, 8, 9, 10}}]}

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