Nothing is known about the crew's strength but the captain Cavendish, has a bounty of 330,000,000. Cavendish gained fame as a "Super Rookie" of his generation one year prior to the "The Worst Generation". 
Suleiman, a notorious war criminal, joined the crew at Dressrosa, presumably making it even stronger.
One year before the beginning of the main storyline, Cavendish and his crew entered the New World, where he made a name for himself. A year later, however, he became overshadowed by the rookies of "The Worst Generation". He resented them heavily for this, and sought to take his revenge by killing them all.
Cavendish entered the Corrida Colosseum, in order to compete for the Mera Mera no Mi. He narrowly lost the fouth quarter of the tournament, and afterwards was turned into a toy by Sugar. When he was freed from the curse by Usopp, he let go of his grudge against Luffy and joined in stopping the Birdcage. In the aftermath of the Birdcage, Suleiman joined Cavendish's crew. Everyone of the wanted warriors, who sided with the Straw Hats gained 50 million belly added to their bounties, including Cavendish.
The crew was later one of the seven groups to request permission to become subordinates of the Straw Hat Pirates. When Luffy declined the offer, Cavendish along with the other representatives pledged themselves to Luffy anyway, becoming part of the Straw Hat Grand Fleet.