On the Earth-22, not much is known about XTC outside that is daughter of Supergirl and Brainiac 5.
Brainiac's Daughter was created by Mark Waid and Alex Ross
Noie: Brainiac's Daughter was based on two songs, 'Brainiac's Daughter' by The Dukes of Stratospher and 'That's Really Super, Supergirl' by XTC. Both bands shared members. Both songs were based on comics continuity.
Kingdom Come / Earth-22
Not much is known of the character. She has a non-speaking role in Kingdom Come and for a while her origins were vague.She was originally conceived as the daughter of Brainiac I and this was published on publicity materials at the time.
However with the comics' theme of the next generation of superheroes at odds with their parents, many thought she was the daughter of Legion lovers, Supergirl and Brainiac 5. Later trade paperback collections and special editions list the Legion origin as correct.
Major Story Arcs
The Death of Brainiac's Daughter
In the story, she shown to be on the side of Superman and his Justice League. She presumably left her parents to go back to the past. She stands at Superman's side throughout and is seen to have a good relationship with other heroes. She flies into the final battle and is presumed dead after the explosion, although she cannot be identified with the other super-heroes' bones.