outer has no recorded synonym. 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. Its one recorded opposite is inner.
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.
being on the outside or further from a center
“spent hours adorning the outer man”
2 of the 3 recorded senses carry no synonym, antonym or related term, so they are not shown above. Every sense, with its definition and examples, is on the full entry for outer.
Synonyms, antonyms and the broader and narrower relations for outer come from Princeton University’s WordNet. Full sources and licences.