I came across this problem in class note but I am stuck:
Let G be a group of order 21, let G' be a group of order 35, and let φ be a homomorphism from G to G'. Assume that G does not have a normal subgroup of order 3. Show that φ(g) = 1 for each element g in G.
Any help or hints would be very much appreciated. Thanks for your time.