Clan Alvaak was a clan formed within the Brotherhood when they were operating with the Emperor's Hammer. Formed by Ronin, leader of the Emperor's Hammer, the clan was comprised of houses Tarentum and Satal Keto before they grew to become their own clans. The Clan did not join the rest of the Brotherhood when they left the Emperor's Hammer in what would later be termed the Exodus.
Here is some information that the Emperor's Hammer had about Clan Alvaak -
Source I
Source II