Hinagiku runs things at Hakuou Academy—she's the student council president and heads the kendo club. She's genuinely skilled with a sword, making her one of the school's standout athletes. When Hayate first shows up completely lost on campus, she takes him to the clocktower, a spot usually reserved for student council members only. She's clearly into him, drawn to his charm, and lets him call her by her first name pretty quickly.
Other characters sometimes call her out for being masculine, at least by typical standards. Miki figures it's because Hinagiku just comes across as cooler than most of the boys around her, plus she was kind of a bully when younger. The kendo skills, the competitive edge, the leadership role—it all feeds into that image. What's funny is that despite all that toughness, she's actually terrified of heights, which doesn't really fit the rest of her personality.
Content compiled by AnimeList.moe from publicly available sources.