Exercise
Let G = S4 acting on itself by conjugation. Which element below has the biggest size stabilizer?
(1,2,3,4)
(1,2,3)
(1,2)(3,4)
(1,2)
False.
The stabilizer is <(1,2,3,4)> of size 4.
False. The stabilizer is
<(1,2,3)> of size 3.
Correct.
The stabilizer is
<(1,3,2,4)> 
(1,2)<(1,2,3,4)>, of size 8.
(1,2)<(1,2,3,4)>, of size 8.
False.
The stabilizer is
<(1,2),(3,4)> of size 4.