sign up vs get together

sign up is not a noun while get together is a noun.

Word	Noun	Adjective	Verb	Adverb
sign up	No	No	Yes	No
get together	Yes	No	Yes	No

As verbs, get together is a hypernym of sign up; that is, get together is a word with a broader meaning than sign up:

sign up: join a club, an activity, etc. with the intention to join or participate
get together: become part of; become a member of a group or organization

Other hypernyms of sign up include fall in, join.

sign up (noun)	get together (noun)
	a small informal social gathering

sign up (verb)	get together (verb)
join a club, an activity, etc. with the intention to join or participate	get together socially or for a specific purpose
engage by written agreement	become part of; become a member of a group or organization
	get people together