Galois group of x^5+x^2+1 over F_2

[@juliefinkjulesheartmagic1111]

Fantastic! Thank you.

[@darkshoxx]

Very cool, I used an ansatz of (x^3+AX^2+BX+C)(X^2+DX+E) = g(X) which leads to a contradiction fairly quickly. The rest is Theorems on finite Galois extensions that I'd probably have to revise :)