group vs team up

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

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

As verbs, team up is a hyponym of group; that is, team up is a word with a more specific, narrower meaning than group:

Other hyponyms of group include team, embed, gang, gang up, pool, brigade.

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