1.6.60 Fields, Groups, Rings

Condition: Let \ (\ Varphi-g about m about r f and z m ~ \ mathbb {z} / 30 \ mathbb {z} \) c \ (\ mathbb {z} / 6 \ mathbb {z} \) such that \ ( \ Operatorname {ker} (\ varphi) = \ {0.6,12,18,24 \} \). Prove that \ (\ varphi- \) is surplus. What possible values can take \ (\ varphi (1) \)?