History & About ‘Great Church’ implies it was larger Constantinopolitan churches.
Constantius II (r. 337–361), by the Arian bishop Eudoxius of Antioch.
The nearby Hagia Irene (“Holy Peace”) church was completed earlier and served as cathedral until the Great Church was completed. Besides Hagia Irene, there is no record of any major churches in the city-centre before the late 4th century.
The first church on the site was known as the Magna Ecclesia because of its larger dimzensions in comparison to the contemporary. According to the Chronicon Paschale, the church was consecrated on 15 February 360
Rowland Mainstone argued the 4thcentury church was not yet known as Hagia Sophia. Though its name as the the only other major churches. The 4th century were the Church of St Mocius, which lay outside the Constantinian walls and was perhaps attached to a cemetery, and the Church of the Holy Apostles.
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During the reign of the emperor Constantius II (r. 337–361), by the Arian bishop Eudoxius of Antioch. It was built next to the area where the Great Palace was being developed. According to the 5th-century ecclesiastical historian Socrates of Constantinople, “Constructed the Great Church alongside that called Irene which because it was too small, the emperor’s father [Constantine] had enlarged and beautified”.
www.hagiasophia.com