Regular orbits of finite primitive solvable groups

Suppose that a finite solvable group G acts faithfully, irreducibly and quasi-primitively on a finite vector space V. Then G has a uniquely determined normal subgroup E which is a direct product of extraspecial p-groups for various p and we denote . We prove that when e⩾10 and e≠16, G will have at least 5 regular orbits on V. We also construct groups with no regular orbits on V when e=8, 9 and 16.