What is the galois group of the polynomial $x^9+x^3+1$? Moreover give the bijection between subgroups and intermediate fields.
Progress
I think the order of the group is 108. But, there are many groups of order 108.
2026-04-04 16:20:24.1775319624
The galois group of the polynomial $x^9+x^3+1$
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The galois group, G, is a semidirect product of the unique non-abelian group, H, of order 27 and exponent 3 with the Klein 4-group, V.