Exterior

Exterior (「エクステリア」, Extelia/Exteria/Exterior) is apparently some device that greatly boosts   Shokuhou Misaki 's power from several hundred meters range and absolutely controlling a maximum of 10 people (or from about 100 people as long as they are doing simple commands) to a range of several kilometers, allowing her to put thousands of people under her control.

Agitate Halation Project Arc (New Testament Volume 7)
At some point during this arc, when Shokuhou reveals to Touma the extent of her powers, she makes it clear that she does not have the increased abilities that Exterior allows her to use. She does not explicitly mention Exterior at all. However, what Misaki told Touma might have also been a lie.

At another point in the arc,  Shokuhou is described as having such a wide application for her powers that she does not have stable control of her powers unless she creates “boundaries” for herself.

This is explained at a point when Misaki is in Learning Core, when it was filled with thousands of students that were all fighting each other. Since at that point in time some areas of Learning Core would be difficult to get into at all, it would have normally been hard to find a specific individual.

However, at this point, Misaki Shokuhou spins around her remote.

Then she grins and suggests “Then how about the first one to reach him gets to do whatever she wants?”

Since she is competing to find Touma within Learning Core, it becomes clear that she could probably easily find Touma in Learning Core.

Furthermore, later on, Misaki is controlling dozens of people at a time in a way that seems to surpass giving simple commands which implies that she can probably still use the abilities that are granted to her by Exterior, even though it is still impossible to determine this fact for certain.