The direct-summation of N gravitational forces is a complex problem for which there is no analytical solution. Dense stellar systems such as galactic nuclei and stellar clusters are the loci of different interesting problems. In this work we present a new GPU, direct-summation N-body integrator written from scratch and based on the Hermite scheme. The first release of the code consists of the Hermite integrator for a system of N bodies with softening. We find an acceleration factor of about ≈ 90 of the GPU version in a single node as compared to the Serial-Single-CPU one. We additionally investigate the impact of using softening in the dynamics of a dense cluster. We study how it affects the two body relaxation, as compared with another code, NBODY6, which uses KS regularization, so as to understand the role of softening in the evolution of the system. This initial release is the first step towards more and more realistic scenarios, starting for a proper treatment for binary evolution, close encounters and the role of a massive black hole.