electrostatics - Electric field due to a line of charge

While deriving the formula for electric field due to an infinitely long wire of uniform charge density using Gauss's law we assume that this field has cylindrical symmetry and there is no component of field along the axis.But how do we know that the field has cylindrical symmetry and there is no component of field along the axis.Why can't there be an axial component of field and what happens if we have a wire of finite length? How does the situation differ from the earlier case?