We develop an abstract framework for studying the strong form of Malle’s conjecture [J. Number Theory 92 (2002), pp. 315–329; Experiment. Math. 13 (2004), pp. 129–135] for nilpotent groups
G
G
in their regular representation. This framework is then used to prove the strong form of Malle’s conjecture for any nilpotent group
G
G
such that all elements of order
p
p
are central, where
p
p
is the smallest prime divisor of
#
G
\# G
.
We also give an upper bound for any nilpotent group
G
G
tight up to logarithmic factors, and tight up to a constant factor in case all elements of order
p
p
pairwise commute. Finally, we give a new heuristical argument supporting Malle’s conjecture in the case of nilpotent groups in their regular representation.