 | 1 | initial version |
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 + 4x^3 + 3x^2 + 7*x + 1
What does mean by 5T5 (S5)
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 following:
Galois group 5T5 (S5) with order 120 of x^5 + 4x^3 4*x^3 + 3x^2 3*x^2 + 7*x + 1
What does mean by 5T5 (S5) (S5) ?
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