The Ottoman Empire was not the largest Muslim Empire as the Umayyad Empire in 749 CE was larger. However, it may be the most influential Muslim Empire, but that is up to the perception of the person discussing it.
The first Muslim Empire was located in Saudi Arabia Under the second Rightful Caliph Hazrat Umar (May Allah be pleased with him). Its capital was Madina Munawara. Later Muslim Empires had their capitals at Kufa, Baghdad, Cordova, Istambol.