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If you give a name to your automorphism group:

sage: A = G.automorphism_group()

Then, you can see all methods that apply to it:

sage: A.<TAB>

where <TAB> stands for the tabulation key.

You can see that there is a cardinality method that answers your question:

sage: A.cardinality()

If you could not find such a method, you could always compute the length of the list you obtained:

sage: len(A.list())