# Recovering a group from it's group algebra over $\mathbb{Z}$

Question: Is it possible to recover a finite group from it's group algebra over $\mathbb{Z}$?

More precisly. By $G_1$ and $G_2$ we denote two finite groups. Let $\mathbb{Z} ( G_1 )$ and $\mathbb{Z} ( G_2 )$ be group algebras. Suppose that $\mathbb{Z} ( G_1 )$ is isomorphic $\mathbb{Z} ( G_2 )$ as algebras. Is $G_1$ isomorphic to $G_2$?

Comment. It is quite obvious that there are not isomorphic finite groups $G_1$ and $G_2$ such that $\mathbb{C} ( G_1 )$ is isomorphic $\mathbb{C} ( G_2 )$. For instance two abelian groups of the same order.