My Little Pony, created by Lauren Faust, is what all the friends have in common.
Although Alex first discovered the show (she was embarassed) Madison and her sister admitted to liking the show, and got the MLP roleplay/cosplay/fangroup (and other things) started.
The group consists of people portraying the pony most like them.
Twilight Sparkle: Taylor
Rainbow Dash: Madison
Pinkie Pie: Alex
Vinyl Scratch: Alia
Some people have multiple pony personalities, and can't be classified besides being epic.