# Infinite charge distribution [duplicate]

I've been thinking about a distribution of charge that does not follow Maxwell's euations, and I can't understand what's wrong with my reasoning. If we have a constant distribution of charge $$\rho(x,y,z)=\rho_0$$ in all space then we have $$\vec\nabla\cdot \vec{E}=\rho_0/\varepsilon_0$$. But the charge' symmetry implies that $$\vec{E}=(0,0,0)$$ in all of space (it as to be the same after a translation or a rotation), so $$\vec\nabla\cdot \vec{E}=0$$. Can someone help me?