group vs assemble

group is a noun but assemble is not a noun.

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

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

Other hypernyms of group include foregather, forgather, gather, meet.

group (noun)	assemble (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)	assemble (verb)
arrange into a group or groups	create by putting components or members together
form a group or group together	collect in one place
	get people together