classify vs group

classify is not a noun while group is a noun.

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

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

classify (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

classify (verb)	group (verb)
arrange or order by classes or categories	arrange into a group or groups
assign to a class or kind	form a group or group together
declare unavailable, as for security reasons