Automorphism group of characteristically polycyclic group is supersolvable

Statement

Let $G$ be a finite group that is a Characteristically polycyclic group (?); in other words, $G$ has a characteristic series where all the successive quotients are cyclic. Then, the automorphism group of $G$ is a Finite supersolvable group (?).

References

Journal references

• Groups with a characteristic cyclic series by John R. Durbin and Merry McDonald, Journal of Algebra, ISSN 00218693, Volume 18, Page 453 - 460(Year 1971): ^{PDF (ScienceDirect)More info}