What is "eoganachta"

The Eóganachta or Eoghanachta were an Irish dynasty centred on Cashel which dominated southern Ireland from the 6/7th to the 10th centuries, and following that, in a restricted form, the Kingdom of Desmond, and its offshoot Carbery, to the late 16th century. By tradition the dynasty was founded by Conall Corc but named after his ancestor Éogan, the firstborn son of the semi-mythological 3rd-century king Ailill Aulom. This dynastic clan-name, for it was never in any sense a 'surname,' should more accurately be restricted to those branches of the royal house which descended from Conall Corc, who established Cashel as his royal seat in the late 5th century.