“You've heard about these guys - "Nightkin", mutants equipped with special cloaking devices. Defeat the Nightkin stationed here so that you can access the ventilation system mainframe.”— Quest description
After reaching the Facilities' mainframe there will be a boss-battle with a group of nightkin. Nightkins are mutants that prefer to avoid being seen, they achieve this with cloaking devices that hide their bodies to near perfect invisibility. There should be about eight to ten of them. After they have been dealt with, access the computer in the center of the room. With the computer the Initiate can open the vault's ventilation shafts. Do that and head out the western door back to the garden.