how would you prove that $Z/30Z$ x $Z/7Z \simeq Z/210Z$ using the semi direct product?
I know that if |G|=pq, (p and q primes) there exist an homomorphism $\phi: C_p --> Aut C_q $ such that G $\simeq$ $C_q$ X $C_p $ (Where 'X' is the semi direct product and $ \simeq$ means 'isomorphic') Thanks !