In reality, while neither Lum, Oyuki nor Benten have ever claimed they were a gang, their mild reputation for getting into trouble has ballooned way out of proportion since they left their old school. Now thanks to the rumor mill, they've become revered as the most cutthroat gang of girls to ever emerge from their school.
It's all a misunderstanding of course but don't try telling that to Sugar, Ginger or Pepper who are far from reasonable. By now they've cultivated a petty rivalry that will not end until they've been proven their betters.
These three twisted brats are rather immature. They're deathly afraid of Lum and company so Instead of initiating a head on fight they seek to beat their eternal rivals by pulling pranks and setting up convoluted schemes aimed at embarrassing them. Their schemes have included, swiping Benten's chain and trying to seduce Ataru from Lum (but even Ataru wasn't interested in them) among other fruitless attempts. But as much as they try to win, they always fail.
This is mostly because despite their claims to greatness, they're ill-equipped to deal with the likes of Lum, Oyuki or Benten. They're nowhere near as smart and their powers are comparitively useless when used more than once. The leader Sugar, the one with her hair in buns has the power to camouflage herself into her surroundings. This makes her seem invisible but it's generally easy to see through the deception. Ginger, the girl with cat ears has the ability to stall her bodily functions in such a way that she can fake being dead. Pepper with the long hair and headband has the odd power to shed the outer layer of her body leaving a gross skin laying behind. Such lame powers barely stand a chance against Lum's electricity, Oyuki's ice powers and Benten's talent for violence. But at least they've got tenacity.
Notes about the names
There's not much to explain here, they're named after spices. However it's interesting that in the Maison Ikkoku movie the names of McEnroe and Salad-chan's puppies were taken from these three girls.
Voices: TARAKO, Chika Sakamoto, Rumiko Ukai
Sugar's voice is series regular TARAKO who also does the voice of Tamiko Shinshi in Patlabor and Taruruuto in Magical Taruruuto-kun.
Ginger's voice is Chika Sakamoto who has played many famous roles, many of which are male characters such as Nuriko of Fushigi Yuugi, Shun Kisaragi of Koko wa Greenwood, Kentarou of Maison Ikkoku, Kazuya of Kimagure Orange Road and Shinta of Gundam Z/ZZ.
Pepper's voice is Rumiko Ukai.