group vs gang up

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

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

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

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

group (noun)	gang 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)	gang up (verb)
arrange into a group or groups	act as an organized group
form a group or group together