We present an experimental analysis of the linear and nonlinear regimes of an attractor of inertial waves in a trapezoidal cavity under rotation. Varying the rotation rate and the forcing amplitude and wavelength, we identify the scaling laws followed by the attractor amplitude and wavelength in both regimes. In particular, we show that the nonlinear scaling laws can be well described by replacing the fluid viscosity in the linear model by a turbulent viscosity, a result that could help in extrapolating attractor theory to geophysically and astrophysically relevant situations. We further study the triadic resonance instability of the attractor which is at the origin of the turbulent viscosity. We show that the typical frequencies of the subharmonic waves produced by the instability behave very differently from previously reported numerical results and from the prediction of the theory of triadic resonance. This behavior might be related to the deviation from the horizontal invariance of the attractor in our experiment in relation to the presence of vertical walls of the cavity, an effect that should be at play in all practical situations.