core group vs cadre

core group and cadre both are nouns.

Word	Noun	Adjective	Verb	Adverb
core group	Yes	No	No	No
cadre	Yes	No	No	No

As nouns, cadre is a hyponym of core group; that is, cadre is a word with a more specific, narrower meaning than core group:

core group (noun)	cadre (noun)
a small group of indispensable persons or things	a nucleus of military personnel capable of expansion
	a small unit serving as part of or as the nucleus of a larger political movement