centre has 25 distinct synonyms spread across 10 of its 11 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
a low-lying region in central France
an area that is approximately central within some larger region
“it is in the center of town”
a point equidistant from the ends of a line or the extremities of a figure
a place where some particular activity is concentrated
“they received messages from several centers”
the choicest or most essential or most vital part of some idea or experience
“the gist of the prosecutor's argument”
the object upon which interest and attention focuses
“his stories made him the center of the party”
a cluster of nerve cells governing a specific bodily process
“in most people the speech center is in the left hemisphere”
a building dedicated to a particular activity
“they were raising money to build a new center for research”
Synonyms, antonyms and the broader and narrower relations for centre come from Princeton University’s WordNet. Full sources and licences.