Although solid ionic compounds donot conduct electricity because there are no free mobile ions or electrons, ionic compounds dissolved in water make an electrically conductive solution. In contrast, covalent compounds do not exhibit any electrical conductivity, either in pure form or when dissolved in water.
We tend to think that conduction only happensin solid materials but this is not true, conduction takes place in solids, liquids and gases, usually though the other forms of heat transfer mask it in all but solid matter. Heat transfer by conduction relies on direct contact between atoms or molecules.