A Center Controller reported they assigned a heading to an aircraft that placed it below the Minimum Vectoring Altitude. The reporter stated sector complexity due to unusual operations; short staffing; management inefficiencies leading to long work periods without breaks contributed to the error.

Narrative

Aircraft X was on a southbound heading for sequence to Runway XX at 3000 ft. and flew into a 3500 ft. MVA about half a mile before turning left on a 070 Heading. At that moment there was a situation developing on the XX Sector between 7 VFR Aircraft in close proximity descending into each other to avoid weather east of ZZZZ. The closeness of the VFRs made it impossible to call traffic due to being unable to identify who was who. At the same time a flight of 2 Aircraft Y's IFR were requesting a low flyby westbound over the coastline. They requested a descent to get below the clouds and requested to cancel IFR. They descended to 7000 ft. and canceled IFR. There was coordination with the Tower to approve their request and it was granted. At this time there was many unusual things happening and I was feeling tired due to being on position for 1:45 minutes. I kept working the sector for the next 30 minutes bringing my total time on a complex sector to 2 and 16 minutes.The Supervisor/CIC (Controller in Charge) was recommended multiple times to cancel training on the XY/XZ Sector due to short staffing; but they decided to continue training regardless. Because of the lack of planning of the rotation me and another controller went over 2 hours on busy/complex sectors. I was finally taken out of position because another Supervisor came in and canceled the training for that trainee to take me out. The previous Supervisor; the one that didn't have a plan; was counting strips and not supervising or helping the situation. Possibly because she isn't certified in XA/XB positions and if it wasn't for the new Supervisor that came in; I would've stayed on position for almost 3 hours.The fact that 2 CPCs called in sick should have been enough reason for cancelling training for the developmental. She was radar qualified on the other sectors and could have helped the rotation to keep everyone safe. The Supervisor insisted that we had the staffing for training going against the recommendation of every CPC on the crew. At the moment when the complexity started picking up; we had nobody to split the sectors to lessen the workload; resulting in an unsafe situation due to saturation and excessive time on position. Also; the lack of knowledge by the Supervisor/CIC due to not being certified on XA/XB positions contributed to the lack of supervision and help to lessen the workload. Training should never come before the safety of the operation and the Supervisor/CIC should be certified on every position that they're supervising to be able to properly step and help in any situation.