Find Galois group of the splitting field of a polynomial
I want to find the splitting field of the polynomial p(x)=x5+4x3+3x2+7x+1∈Q[x]. I have used the following source code:
K.<alpha> = NumberField(x^5+4x^3+3x^2+7*x+1)
G = K.galois_group()
G
The output is the following:
Galois group 5T5 (S5) with order 120 of x^5 + 4*x^3 + 3*x^2 + 7*x + 1
What does mean by 5T5 (S5)
?