give an example of a galois group

apple2009

For each finite group G with |G|≤7, give an example of an equation whose Galois group over Q is isomorphic to G.

TheArtofSymmetry

For each finite group G with |G|≤7, give an example of an equation (polynomial over Q?) whose Galois group over Q is isomorphic to G.
See 1 and 2.

For example, a corresponding polynomial over Q for a galois group of order 4 is x^5-1 since $$\displaystyle |(\mathbb{Z}/5\mathbb{Z})^\times|=4$$.

For an order 3, you might need to use A_3=Z_3. You can find the corresponding polynomial in the above link.