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>Wonder Infantry
A hi-tech team with cloaking devices/illusionary disguises that allow them to suddenly flash-mob their targets despite their gaudy outfits (Retro-futuristic, in the vein of Team Galactic; lots of moon boots, visors, LED lights and miniskirts)
They don't seem to have concrete goals, though; every time you fight them, they claim to be conducting 'experiments', social or otherwise, and are generally quite affable; they leave peacefully whenever you beat them up, and they actually help you out at key moments a couple times over the course of your journey.
Tactics-wise, they use a staggering array of Pokemon, many of which are gimmicky or obscure, and they introduce players to things like Room and Terrain effects and double/triple battles; the lead scientist admins have even more outlandish gimmicks like Inverse battles.
Ultimately, however, their leader is a charming young woman who happens to be your secondary rival and from the future; their goal is to avert an incoming cataclysm caused by rampaging legendary Pokemon which you completely cock up once you defeat her and destroy the machine at the heart of their base, forcing you to work together to save the region before ultimately parting ways.