Final answer:
The group within the Ottoman Empire known for its social and political authority, composed of the sultan's female companions and relatives, was the Harem.
Step-by-step explanation:
The name of the group within the Ottoman Empire composed of the wives, servants, female relatives, and the sultan's concubines, which played an important social function within the Ottoman court and demonstrated considerable political authority in Ottoman affairs, was B) Harem.
The Ottoman harem was not merely the sultan's private family space but was also a complex social institution. It had its own hierarchy and rules, where women could exert great influence and, in certain periods, even participate in state politics through their relationships with the sultan or as mothers of future sultans. The institution known as the Sultanate of Women signified the era when women in the harem, such as wives or mothers of the reigning sultan, had substantial influence at court and were involved in political maneuvering.