Q: D₄ acts on square's vertices. Find the orbit and stabilizer of a vertex. Orbit of vertex v: all 4 vertices (rotations move it everywhere!)! Stabilizer: {e, reflection across diagonal through v} (order 2!). Orbit-stabilizer: |orbit|×|stab| = 4×2 = 8 = |D₄| ✓! (Counting via actions!)