What is the most ancient gruop of vertebrates?

fish

The vertebrates have a nebulous starting point. There are some chordates that have more of a notochord than a true vertebrate column. Some taxicologists are more comfortable saying that a Coelacanth has a notochord rather than a vertebrate column when clearly the vertebrate are present in this animal.

So its is a matter of your own definition. One could say 'at a stretch' that the hagfish and lamprey are the most ancient vertebrates.