Exercise
Recall the permutation representations C (conjugation), L (left multiplication), R (right inverse multiplication) of an arbitrary group G. Which of these are always transitive?
none
L and R
all three.
False.
Multiplying e from the left by g gives g.
Correct.
No.
From geg-1 = e it follows that {e} is an
orbit of the C action.
So, for all nontrivial G, the permutation representation C is not transitive.