Final answer:
The Motown group in question is The Temptations, known for their popular hits and influential dance choreography, as well as tragedies among members.
Step-by-step explanation:
The quintessential Motown group mentioned in the question that is known for hits like "My Girl," "Just My Imagination," "Papa Was a Rolling Stone," and "I Wish It Would Rain," and for a rich blend of dance moves and choreography during 1964-1968 with their original line-up, is The Temptations.
This group suffered from various personal tragedies, including members facing substance abuse, alcoholism, and health issues leading to their deaths. The Temptations are distinguished for their significant impact on the music of that era and are not to be confused with other groups like The Supremes, The Four Tops, or The Jackson 5, the latter known for their large as a symbol of Black Pride when appearing on shows like Soul Train.