Property on homomorphism between finite groups I was reading some lecture notes on homomorphism between finite groups and intuitively it appeared to me that for a $\phi$ an homomorphism $G \rightarrow H$, we should have:
$$|\,\textrm{Im}(\phi)\,| =  \frac{|\,G\,|}{|\,\textrm{ker}(\phi)\,|}$$
where $| . |$ stands for order. Is this right? If yes, is there a short demonstration for?

ker($\phi$) is a normal subgroup of G, so G/ker($\phi$) is well defined and |G/ker($\phi$)|=|G|/|ker($\phi$)|.
Thanks to "the first isomorphism theorem", there exists an isomorphism between Im($\phi$) and G/Ker($\phi$) moreover |Im($\phi$)|=|G|/|Ker($\phi$)|
