We detail the construction of the most general asymptotically flat, stationary, rotating, nonextremal, dyonic black hole of the four-dimensional N=2 supergravity coupled to 3 vector multiplets that describes the STU model. It generates through U dualities the most general asymptotically flat, stationary black hole of N=8 supergravity. We develop the solution generating technique based on SO(4,4)/SL(2,R)4 coset model symmetries, with an emphasis on the 4-fold permutation symmetry of the gauge fields. We indicate how previously known nonextremal and extremal solutions of the STU model are recovered as limiting cases. Several properties of the general black hole solution are discussed, including its thermodynamics, the quadratic mass formula, the Bogomolny-Prasad-Sommerfield limit, the slow and fast extremal rotating limits, its properties in regards to the Kerr/conformal field theory correspondence, its Killing tensors and the separability of geodesic motion and probe scalars.