Number of sylow subgroups

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Because all Sylow subgroups are conjugate, it is enough to find one and compute its normalizer: the answer will be the index of this normalizer in G. GAP is the most convenient way to do it which is interfaced in SageMath

sage: G = libgap.DicyclicGroup(12)  # a group
sage: p = 2  # a prime
sage: H = libgap.SylowSubgroup(G, p)
sage: N = libgap.Normalizer(G, H)
sage: libgap.Index(G, N)
3

If you have a PermutationGroup defined from sage, you can use it in place of G above.