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This code works fine:

sage: Q1.<a> = NumberField(x^3- 2)
sage: Q1
Number Field in a with defining polynomial x^3 - 2
sage: G1=Q1.galois_group('pari')
sage: G1
Galois group PARI group [6, -1, 2, "S3"] of degree 3 of the Number Field in a with defining polynomial x^3 - 2

The other fields do not play a role in your error. Your mistake is to have written

sage: G1.<m>=Q1.galois_group('pari')

since the syntax where you put ".<m>" after the identifier being defined is a short-cut only works when that object has generators which can be accessed in a certain way. You can see how Sage is preparsing the incorrect line like this:

sage: preparse("G1.<m>=Q1.galois_group('pari')")
"G1 = Q1.galois_group('pari', names=('m',)); (m,) = G1._first_ngens(1)"

So the Galois group G1 is being assigned OK, but does not have a function of the name expected by that input syntax. In fact G1 has very few functions.