Final answer:
The spirochaetes are characterized by their unique flagellar structure contained within an outer sheath, which allows them to have a distinctive corkscrew motion.
Step-by-step explanation:
The group characterized by unusual flagella contained within a structure called the outer sheath is B. Spirochaetes. These are motile, spiral bacteria that possess flagella running lengthwise in the periplasmic space between the inner and outer membrane. Unlike other bacteria, spirochaetes have flagella which remain in the periplasmic space and are enclosed by an outer sheath, allowing them to move with a corkscrew-like motion