  We show that any Carnot group contains a closed nowhere dense set which has
measure zero but is not $\sigma$-porous with respect to the
Carnot-Carath\'eodory (CC) distance. In the first Heisenberg group we observe
that there exist sets which are porous with respect to the CC distance but not
the Euclidean distance and vice-versa. In Carnot groups we then construct a
Lipschitz function which is Pansu differentiable at no point of a given
$\sigma$-porous set and show preimages of open sets under the horizontal
gradient are far from being porous.
