A comprehensive study of the absorption transitions leading to the 5pσ, 6pσ and 7pσ Rydberg states of H2 is presented which includes rovibronic level energies, line intensities and widths. The analysis of the experimental data is carried out with the help of multichannel quantum defect theory implemented here purely from first principles. Numerous new assignments are reported and some older assignments are corrected. The overall agreement between experiment and theory is very good. In particular, absorption line (resonance) energies are reproduced to within 1 cm−1.