My female flares like crazy, far more than my male. She will flare if she catches her reflection in anything, and will go crazy trying to get at her reflection if I put a mirror up to her tank. She will also flare and jump up at things above the water (other than my magical hand of food - she waits patiently for me to drop pellets.)
I have a feeling she would chase down and kill any other females if I tried to put her in a sorority.
My male, on the other hand, is pretty mellow. He rarely flares and never jumps.