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You can use the PermutationGroup to create a permutation group from specific elements (cycle notation). And then you can check if a particular element is in the group:

sage: G = PermutationGroup([[(1,2,3),(4,5)],[(3,4)]])
sage: G
Permutation Group with generators [(3,4), (1,2,3)(4,5)]
sage: (3,4) in G