Isomorphism between two finite order groups

Question

So, I am self-studying algebra. Thus, I gave myself this exercise: knowing that there is one abelian group of order $5$ (namely $\mathbb{Z}_5$), find an isomorphism between $\mathbb{Z}_5$ and this group: $$ \begin{array}{c|lcr} \cdot & 0& 1 & 2& 3 &4 \\ \hline 0 & 0 & 1 & 2 & 3 & 4 \\ 1 & 1 & 4& 0 & 2 & 3 \\ 2 & 2 & 0 & 3 & 4 & 1 \\ 3 & 3 & 2 & 4 & 1 & 0 \\ 4 & 4 & 3 & 1 & 0 & 2 \\ \end{array} $$ All my efforts have failed. I tried to define a permutation, but this gave me the exact same group. I'm very confused; help is welcome.

Answer 1

Thanks to the helpful advice from the lovely people in the comments, I figured it out. Define the map $$ \begin{pmatrix} 0 & 1 & 2 & 3 & 4 \\ 0 & 1 & 4 & 3 & 2 \\ \end{pmatrix} $$ and it follows immediately.