Doctrinally, they heretically believe Mary to be present in the Eucharist and the whole foundation of their community is based on Jesus allegedly transferring the primacy from Rome to their new see (contra what was defined at the First Vatican Council).
Their origin stems from certain young seers in the 60s. The bishop dismissed their claims, and they eventually abandoned them–but another guy took them up and held himself out as the new seer. He eventually made himself Pope, and here we are. When he died, they canonized him as Gregrory the Very Great, which kinda tells you all you need to know if the above wasn’t enough. It seems his successors like naming themselves Peter these days (they are on Peter III). They used to have more bishops than laity, but I think they’ve trimmed it down.
Ironically, they also have their own Palmarian sedevacantists who believe the main Palmarians have gone off the rails.