Find Galois group of the splitting field of a polynomial

I want to find the splitting field of the polynomial $$p(x)=x^5+4x^3+3x^2+7x+1 \in \mathbb Q[x].$$ I have used the following source code:

K.<alpha> = NumberField(x^5+4x^3+3x^2+7*x+1)

G = K.galois_group()

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) ?

1 Answer

Sort by » oldest newest most voted

5733 ●5 ●37 ●123

See https://www.lmfdb.org/GaloisGroup/5T5 for details of what is 5T5 group. S5 seems to be the CHM label introduced in this paper.

Please start posting anonymously - your entry will be published after you log in or create a new account.

1 follower

Asked: 2022-10-14 14:57:58 +0200

Seen: 195 times

Last updated: Oct 14 '22