group vs forgather

group is a noun but forgather is not a noun.

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

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

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

group (noun)	forgather (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)	forgather (verb)
arrange into a group or groups	collect in one place
form a group or group together