group vs classify

group is a noun but classify is not a noun.

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

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

Other hypernyms of group include assort, class, separate, sort, sort out.

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