This paper continues the investigations of this series. Suppose that
G
=
A
N
S
G = ANS
where S and NS are normal subgroups of G. Suppose that
(
|
A
|
,
|
N
S
|
)
=
1
(|A|,|NS|) = 1
, S is extraspecial, and
S
/
Z
(
S
)
S/Z(S)
is a faithful minimal module for the subgroup AN of G. Assume that k is a field of characteristic prime to
|
G
|
|G|
and V is a faithful irreducible
k
[
G
]
{\mathbf {k}}[G]
-module. The structure of G is discussed in the minimal situation where N is cyclic, A is nilpotent, and
V
|
A
V{|_A}
does not have a regular A-direct summand.