Take for instance the example:
G = NumberField(x^5 + 15*x + 12, 't').galois_group(type="pari"); G
This gives an output:
Galois group PARI group [20, -1, 3, "F(5) = 5:4"] of degree 5 of the Number Field in t with defining polynomial x^5 + 15*x + 12
So I wonder what is the meaning of [20, -1, 3, "F(5) = 5:4"]. Is it some kind of permutation?
The relevant page of the documentation doesn't clarify it.