Abu al-Abbas was the first Abbasid caliph and descended from Muhammad's uncle. He was a Sunni Muslim, but allied readily with Shia Muslims and also non-Arab Muslims, particularly Persian converts who were resentful of the Umayyad Dynasty's preference to Arab Muslims. He began "a campaign of extermination against the Umayyads, the Alids, other Abbāsid leaders who had become too popular, and all other claimants to power. He named himself as-Saffāḥ, “the blood-shedder,” because of his savage attacks. He established a firm legal and dynastic base for the ʿAbbāsids." After extinguishing most of the Umayyad clan in battle, he invited the remaining members to a banquet under the guise of reconciling their differences but he slaughtered all of them.
This is not the Abbasid Caliphate at the time of Abu al-Abbas but at its greatest extent.
See pg. 356 in T&E for further details.