Can dissipationless N-body simulations be used to reliably determine the structural and substructure properties of dark matter halos? A large simulation of a galaxy cluster in a cold dark matter universe is used to increase the force and mass resolution of current "high-resolution simulations" by almost an order of magnitude to examine the convergence of the important physical quantities. The cluster contains similar to5 million particles within the final virial radius, R-vir similar or equal to 2 MPC (with H-0 = 50 km s(-1) Mpc(-1)), and is: simulated using a force resolution of 1.0 kpc (equivalent to 0.05% of R-vir); the final virial mass is 4.3 x 10(14) M-., equivalent to a circular velocity of v(circ) (GM/R)(1/2) similar or equal to 1000 km s(-1) at the virial radius. The central density profile has a logarithmic slope of -1.5, identical to lower resolution studies of the same halo, indicating that the profiles measured from simulations of this resolution have converged to the "physical" limit down to scales of a few kpc (similar to0.2% of R-vir). In addition, the abundance and properties of substructure are consistent with those derived from lower resolution runs; from small to large galaxy scales (v(circ) > 100 km s(-1), m > 10(11) M-.), the circular velocity function and the mass function of substructures can be approximated by power laws with slopes of similar to -4 and similar to -2, respectively. At the current resolution, overmerging (a numerical effect that leads to structureless virialized halos in low-resolution N-body simulations) seems to be globally unimportant for substructure halos with circular velocities of v(circ) > 100 km s(-1) (similar to 10% of the cluster's v(circ)). We can identify subhalos orbiting in the very central region of the cluster (R less than or similar to 100 kpc), and we can trace most of the cluster progenitors from high redshift to the present. The object at the cluster center (the dark matter analog of a cD galaxy) is assembled between z = 3 and z = 1 from the merging of a dozen halos with v(circ) greater than or similar to 300 km s(-1). Tidal stripping and halo-halo collisions decrease the mean circular velocity of the substructure halos by approximate to 20% over a 5 billion yr period. We use the sample of 2000 substructure halos to explore the possibility of biases using galactic tracers in clusters: the velocity dispersions of the halos globally agree with the dark matter within less than or similar to 10%, but the halos are spatially antibiased, and in the very central region of the cluster (R/R-vir < 0.3) they show positive velocity bias (b(v) <equivalent to> sigma (v3D,halos)/sigma (v3D,DM) similar or equal to 1.2-1.3); however, this effect appears to depend on numerical resolution.
