PARI Group Labelling
I have a Galois group that I'm tying to determine:
f = x^5 - 792*x^4 + 71280*x^3 + 39517632*x^2 - 7519640832*x + 314605513728
d = 3
A = -9504*d^2
B = 365904*d^3
K.<a> = NumberField(f)
R.<y> = K[]
g = y^2 - a^3 - A*a - B
L.<z> = NumberField(y^2 - a^3-A*a-B)
G = L.galois_group()
I have a couple of issues: When I type G[1], it says
GaloisGroup_v1 is not subscriptable
The second is the output for G says
[10,-1,1,'C(10)=5[x]2']
I know this is the PARI label and the last entry is the GAP 4 label. But for the life of me I cannot find anywhere where it explicitly tells me what C(10)=5[x]2 means.
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