1) chief command, rule, sovereignty
1a) of the reign of a Roman emperor
Part of Speech: noun feminine
From G2232; government, that is, (in time) official term: - reign.
These two sites give similar information, with the definition from several dictionaries and statistics on the use of the word.
Perseus Digital Library
University of Chicago's Logion lexicon
Thayer's dictionary plus other information.
From this site's dictionary (in Italian)
Click on the first column to search for that word as a form of the root ἡγεμονία; click on the second column to search for that grammatical form of the root ἡγεμονία; click on the third column to search for that word and grammatical form; click on the total to search for the root ἡγεμονία.