The ornamental design for a compactsterilizingrack, as shown and described.
FIG. 1 is a front, right side perspective view of the compact sterilizing rack;
FIG. 2 is a back elevational view of the compact sterilizing rack;
FIG. 3 is a top plan view of the compact sterilizing rack;
FIG. 4 is a right side elevational view of the compact sterilizing rack;
FIG. 5 is a left side elevational view of the compact sterilizing rack; and,
FIG. 6 is a bottom plan view of the compact sterilizing rack.
The broken lines are included for the purpose of illustrating unclaimed portions of the compact sterilizing rack and form no part of the claimed design.