  We study the influence of the various parameters of scenarios of large-scale
structure formation on properties of galaxy clusters, and investigate which
cluster properties are most sensitive to these parameters. We present a set of
large N-body simulations and derive the intrinsic properties of galaxy clusters
in these simulations, which represent a volume of $256^3 h^{-3}$ Mpc^3. The
cosmological scenarios studied differ in either the shape of the power spectrum
of initial fluctuations, its normalization, the density parameter $\Omega_{0}$,
or the Hubble parameter $H_{0}$. Between each of the simulations, only one
parameter is set differently, so that we can study the influence of that
parameter on the cluster properties. The cluster properties that are studied
are the mass, line-of-sight velocity dispersion, peculiar velocity, intrinsic
shape, and orientation with respect to its surroundings. $\sigma_{8}$ has a
large impact on the cluster properties. The latter, viz. the cluster number
density, mass, line-of-sight velocity dispersion and peculiar velocity, are
also determined by $\Omega_{0}$, though somewhat less. Other parameters, such
as $H_{0}$, the tilt of the initial fluctuation spectrum, and the exact shape
of this spectrum, are generally less important. Unlike the other cluster
properties studied, the peculiar velocity is found to depend on all parameters
of the formation scenario. Using scaling relations between the average
properties of the cluster sample and the parameters of the formation scenario,
one may try and interpolate between the scenarios studied here in order to find
the parameters of the scenario that is most consistent with the data.
