core has 20 distinct synonyms spread across 5 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 small group of indispensable persons or things
“five periodicals make up the core of their publishing program”
the choicest or most essential or most vital part of some idea or experience
“the gist of the prosecutor's argument”
a cylindrical sample of soil or rock obtained with a hollow drill
an organization founded by James Leonard Farmer in 1942 to work for racial equality
(computer science) a tiny ferrite toroid formerly used in a random access memory to store one bit of data; now superseded by semiconductor memories
“each core has three wires passing through it, providing the means to select and detect the contents of each bit”
the chamber of a nuclear reactor containing the fissile material where the reaction takes place
a bar of magnetic material (as soft iron) that passes through a coil and serves to increase the inductance of the coil
remove the core or center from
“core an apple”
Synonyms, antonyms and the broader and narrower relations for core come from Princeton University’s WordNet. Full sources and licences.