A regular hexagon has rotational symmetry and can be rotated about its center. The rotations that map the hexagon onto itself are multiples of \( \frac{360^\circ}{n} \), where \( n \) is the number of sides (which is 6 for a hexagon).
Calculating this gives: \[ \frac{360^\circ}{6} = 60^\circ \]
The rotations that map the hexagon onto itself are therefore:
- \( 0^\circ \) (no rotation)
- \( 60^\circ \)
- \( 120^\circ \)
- \( 180^\circ \)
- \( 240^\circ \)
- \( 300^\circ \)
The largest degree of rotation, excluding \( 360^\circ \), that would turn a regular hexagon onto itself is:
\[ \boxed{300^\circ} \]