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Because all Sylow subgroups are conjugate, it is enough to find one and compute its normalizer. GAP is the most convenient way to do it which is interfaced in SageMath

sage: G = libgap.DicyclicGroup(12)
sage: H = libgap.SylowSubgroup(G, 2)
sage: libgap.Normalizer(G, H).Size()
4

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

Because all Sylow subgroups are conjugate, it is enough to find one and compute its normalizer. 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)
sage: H = libgap.SylowSubgroup(G, 2)
sage: G.Size() / libgap.Normalizer(G, H).Size()
4
3

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

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)
sage: H = libgap.SylowSubgroup(G, 2)
sage: G.Size() / libgap.index(G, libgap.Normalizer(G, H).Size()
H))
3

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

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

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

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, libgap.Normalizer(G, H))
N)
3

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

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, libgap.Index(G, N)
3

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