We study the energy level structure of the Tavis-Cumming model applied to an ensemble of independent magnetic spins s =1/ 2 coupled to a variable number of photons. Rabi splittings are calculated and their distribution is analyzed as a function of photon number n max and spin system size N. A sharp transition in the distribution of the Rabi frequency is found at n max N. The width of the Rabi frequency spectrum diverges as N at this point. For increased number of photons n max N, the Rabi frequencies converge to a value proportional to n max. This behavior is interpreted as analogous to the classical spin-resonance mechanism where the photon is treated as a classical field and one resonance peak is expected. We also present experimental data demonstrating cooperative, magnetic strong coupling between a spin system and photons, measured at room temperature. This points toward quantum computing implementation with magnetic spins, using cavity quantum-electrodynamics techniques.