Well, her arrogance is her most notable quality in this great dystopian novel. In addition, you might want to consider the following aspects about her. She likes to deliver sermon-like orations to explain how she sees the world. The amount of dialogue that is given to her is amazing, and David variously describes what she says as an "apologia" and a "disquisition." Her "rhetorical style" is something that David and the others struggle to keep up with, and, interestingly, we could argue that the Sealand woman finds a parallel with David's father, as both are passionately evangelical about what they believe, even though their beliefs are completely different.
However, in addition to these more negative traits, she is shown to be sympathetic and compassionate. Note the way that she carefully explains why they are unable to go to Waknuk and collect Rachel, and what David says about her afterwards:
There was a pause while we appreciated the situation. She had made it clear enough, and she sat back, a motionless figure in her gleaming white suit, her knees drawn up and her hands clasped round them, waiting sympathetically and patiently for us to accept the facts.
However, this positive description of her is then somewhat undercut by her matter-of-fact description of how she has just slaughtered all of the other people in the Fringes. Thus, although the Sealand woman is shown to have some positive traits, at the same time perhaps we can argue that her negative traits are more notable.