group vs assort

group is a noun but assort is not a noun.

Word	Noun	Adjective	Verb	Adverb
group	Yes	No	Yes	No
assort	No	No	Yes	No

As verbs, assort is a hypernym of group; that is, assort is a word with a broader meaning than group:

Other hypernyms of group include class, classify, separate, sort, sort out.

group (noun)	assort (noun)
any number of entities (members) considered as a unit
a set that is closed, associative, has an identity element and every element has an inverse
(chemistry) two or more atoms bound together as a single unit and forming part of a molecule

group (verb)	assort (verb)
arrange into a group or groups	arrange or order by classes or categories
form a group or group together	keep company with; hang out with