team up vs group

team up is not a noun while group is a noun.

Word	Noun	Adjective	Verb	Adverb
team up	No	No	Yes	No
group	Yes	No	Yes	No

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

Other hypernyms of team up include aggroup.

team up (noun)	group (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

team up (verb)	group (verb)
form a team	arrange into a group or groups
	form a group or group together