1. Let G be the group of rotations of a regular tetrahedron.

(i) Prove that |G| = 12.

(ii) Identify G as a subgroup of S4, by labelling the vertices or otherwise.

(iii) Find a subgroup N of G of order 4 and write down the (distinct) left and right cosets of N in

G. Deduce that N is a normal subgroup of G and identify the quotient group G/N.

(iv) Find a subgroup H of G of order 3. Is H normal in G?