The First Murray Group was the iteration of the League of Extraordinary Gentlemen lasting from May, 1898 to July of that same year. It consisted of Mina Murray, Allan Quatermain, Captain Nemo, Dr. Henry Jekyll/Edward Hyde, and Hawley Griffin. With the assistance of the League's "handler," Campion Bond, Mina Murray was largely responsible for assembling the group, working initially under Professor James Moriarty and then Mycroft Holmes.
This League was responsible for defeating The Doctor and Moriarty during an aerial war they waged over London and assisted in the efforts to stop the invasion of the Martians, which led to the deaths of Griffin and Hyde. They ultimately disbanded after Nemo resigned in protest after discovering that "disease bombs" were dropped on the civilian populace in order to eliminate the Martian threat.
Murray and Quatermain remained members of MI5 for several decades, however, and were later responsible for the formation of the Second Murray Group.