1) to be grandiloquent
2) to boast great things, to bear one's self loftily in speech or action
Part of Speech: verb
From a compound of G3173 and αὐχέω aucheô (to boast; akin to G837 and G2744); to talk big, that is, be grandiloquent (arrogant, egotistic): - boast great things.
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 αὐχέω; click on the second column to search for that grammatical form of the root αὐχέω; click on the third column to search for that word and grammatical form; click on the total to search for the root αὐχέω.