The aftermath of an Endbinger battle is anything but orderly - and so at just the right moment a body might be left unwatched long enough for a portal to open and a hand to reach out and touch it.
"There are six cellblocks for each gender. You can move between the male and female sections, but most people don't. There's also space farther down without people in charge. I can tell you what I know about each place if you'd like?"
"Please. I can't personally make use of the information but it seems like useful context."
Then she can list them, starting with the ones that actually have substantial amounts of control over their cellblock: Lustrum (extremely... ideological, in a way that makes it difficult if she decides you don't believe the right things), the Fairy Queen (people behave well, you just need to not get her in particular annoyed at you which isn't nearly so hard for a lot of people), Marquis (his cellblock involves more random violence than the other two but it's only violence that fit within the rules he's set down), Crane the Harmonius (running a cult which doesn't interact with outsiders much), and Teacher (nice, but in a way where everyone is an unclear degree of mind controlled). The other cell blocks have more random violence, with the places without leaders being tantamount to death sentences for all but the strongest of capes.
"-I think that's all the most important difference between the cellblocks but I might be forgetting something."
"You may." She summons the Refuse Collector who can provide Lorica with a child's electronic keyboard and a window mounted AC unit.
That'll keep her busy for a while. Mostly building tools rather than directly useful things. Hopefully she can house Rete soon.
Dragon returns with an answer from her superiors eventually.
"They won't make an exception - I'm sorry. I took it to Chief Director Costa-Brown but she refused to overrule my superiors."