As always, comments (particularly corrections) are welcome.
Mycroft Holmes (Note: All quotations are from GREE unless specified otherwise.)
According to Sherlock Holmes, his brother, Mycroft, is his superior in observation and deduction but “will not even go out of his way to verify his own solutions, and would rather be considered wrong than take the trouble to prove himself right.” He rarely goes anywhere but his Whitehall office, the Diogenes Club (of which he was a founding member), and his Pall Mall lodgings, hence Sherlock’s surprise whenever Mycroft appears at 221 B.
Mycroft is seven years older than Sherlock, and very stout, but there is nonetheless a strong resemblance between the brothers. As Watson puts it, “his face, though massive, had preserved something of the sharpness of expression which was so remarkable in that of his brother. His eyes, which were of a peculiarly light, watery gray, seemed to always retain that far-away, introspective look which I had only observed in Sherlock’s when he was exerting his full powers.” This kinship is underscored by their mutual respect and trust: Mycroft recommends Sherlock as the best man for the case in “The Greek Interpreter” and “The Adventure of the Bruce-Partington Plans,” while Sherlock relies on Mycroft’s aid during his flight from London and subsequent travels.
Holmes at first tells Watson that his brother “audits the books in some of the government departments,” but later reveals that Mycroft’s ability to recall and correlate data enables him to act as a clearinghouse for government policy, making him “the most indispensable man in the country” (BRUC). Fanonically, the latter statement is often interpreted to mean that Mycroft is the head of an espionage network.