  The moons of giant planets are believed to form in situ in Circumplanetary
Discs (CPDs). Here we present an N-body population synthesis framework for
satellite formation around a Jupiter-like planet, in which the dust-to-gas
ratio, the accretion rate of solids from the Protoplanetary Disc, the number,
and the initial positions of protosatellites were randomly chosen from
realistic distributions. The disc properties were from 3D radiative simulations
sampled in 1D and 2D grids and evolved semi-analytically with time. The N-body
satellitesimals accreted mass from the dust component of the disc, interacted
gravitationally with each other, experienced close-encounters, both scattering
and colliding. With this improved modeling, we found that about $15\%$ of the
resulting population is more massive than the Galilean one, and only $8.5\%$
were in resonances. The moons reach Europa's mass most frequently in $10^5$
years. In $10\%$ of the cases, moons are engulfed by the planet, and $1\%$ of
the satellite-systems lose at least 1 Earth-mass into the planet, contributing
to the giant planet's envelope's heavy element content. In $1\%$ of cases, we
found eccentricities and inclinations of moons above 0.1. We examined the
differences in outcome between the 1D and 2D disc models and used machine
learning (Randomized Dependence Coefficient together with t-SNE) to compare our
population with the Galilean system. Detecting our population around known
transiting Jupiter-like planets via transits and TTVs would be challenging, but
$14\%$ of the moons could be with an instrumental transit sensitivity of
$10^{-5}$.
