We suppose that $G_1, G_2$ are finite groups with order $100$ and $f_1: G_1 \rightarrow \mathbb{Z}_{1200}, f_2: G_2 \rightarrow \mathbb{Z}_{120}^*$ are group homomorphisms. Which of the following statements are certainly wrong?
- $|Ker(f_1)|=10$
- $|Im(f_1)|=160$
- $|Ker(f_2)|=30$
- $|Im(f_2)|=20$
Could you give some hints what I am supposed to do?