Erbium ions in crystals show considerable promise for the technologies that will form the backbone of future networked quantum information technology. Despite advances in leveraging erbium’s fibre-compatible infrared transition for classical and quantum applications, the transitions are, in general, not well understood. We present detailed absorption and laser site-selective spectroscopy of the C3v(O2−) centre in CaF2 :Er3+ as an interesting erbium site case study. The 4 I15∕2Z1 → 4 I13∕2Y1 transition has a low-temperature inhomogeneous linewidth of 1 GHz with hyperfine structure observable from the 167Er isotope. A parametrized crystal-field Hamiltonian is fitted to 34 energy levels and the two ground state magnetic splitting factors. The wavefunctions are used to perform a transition intensity analysis and electric-dipole parameters are fitted to absorption oscillator strengths. Simulated spectra for the 4 I11∕2 → 4 I15∕2 and 4 I13∕2 → 4 I15∕2 inter-multiplet transitions are in excellent agreement with the experimentally measured spectra. The 4 I13∕2 excited state lifetime is 25.0 ms and the intensity calculation is in excellent agreement with this value.