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Find Galois group of the splitting field of a polynomial

asked 2022-10-14 14:57:58 +0100

Mabudmath gravatar image

updated 2022-10-14 17:26:42 +0100

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()

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) ?

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answered 2022-10-14 17:33:37 +0100

Max Alekseyev gravatar image

updated 2022-10-14 17:40:13 +0100

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.

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Asked: 2022-10-14 14:57:58 +0100

Seen: 152 times

Last updated: Oct 14 '22