WordNet records no synonym and no antonym for sociality. It is the only member of its synset, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
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.
the tendency to associate with others and to form social groups
“mammals as a class are not strong on sociality”
Synonyms, antonyms and the broader and narrower relations for sociality come from Princeton University’s WordNet. Full sources and licences.