sympathize vs sympathizer

sympathize is not a noun while sympathizer is a noun.

Word	Noun	Adjective	Verb	Adverb
sympathize	No	No	Yes	No
sympathizer	Yes	No	No	No

sympathize (noun)	sympathizer (noun)
	someone who shares your feelings or opinions and hopes that you will be successful
	a person who commiserates with someone who has had misfortune

sympathize (verb)	sympathizer (verb)
be understanding of
to feel or express sympathy or compassion
share the feelings of; understand the sentiments of