  We analyse the existence and the stability of the ground states of the
one-dimensional nonlinear Schr\"{o}dinger equation with a focusing power
nonlinearity and a defect located at the origin. In this paper a ground state
is defined as a global minimizer of the action functional on the Nehari
manifold and the defect considered is a F\"{u}l\"{o}p-Tsutsui $\delta$ type,
namely a $\delta$ condition that allows discontinuities. The existence of
ground states is proved by variational techniques, while the stability results
from the Grillakis-Shatah-Strauss theory.
