alphabet vs alphabetical

alphabet is a noun but alphabetical is not a noun.

Word	Noun	Adjective	Verb	Adverb
alphabet	Yes	No	No	No
alphabetical	No	Yes	No	No

alphabet (noun)	alphabetical (noun)
the elementary stages of any subject (usually plural)
a character set that includes letters and is used to write a language

alphabet (adjective)	alphabetical (adjective)
	arranged in order according to the alphabet
	relating to or expressed by a writing system that uses an alphabet