Stand by for the real experts, but I find that 1.1 Vs to be a little lower than I would generally expect from common GA aircraft. Perhaps that is valid for higher powered aircraft. Reviewing my 1981 C-172RG manual, Vs at MTOW is 55.5 KCAS. (interpolated halfway between fwd and aft CG limits) SL Vx is published as 67 KIAS, (allthough 63 KIAS is the recommended obstacle clearance speed.) which when corrected to CAS is 68 KCAS. 68/55.5 = 1.225. The listed Vs assumes power off. The actual stall speed at full power is (by demonstration) somewhat lower than that due to prop thrust induced lift at the wing roots and the vertical component of thrust in a nose-high attitude. I would suspect that with a great deal more power available, the ratio of Vx/Vs would reduce signifigantly.
In fact, I saw Wayne Handley fly from a 90 degree nose up hover and accelerate straight up in his Turbo Raven at the Reno air races a few weeks before he crashed it at another airshow back in '99. A 90 degree angle of climb in a turboprop! A PT-6A in a very light airplane is a wonderous thing.
But back to the subject. The actual Vx for a particular prop aircraft would occur at the speed where the most excess thrust is available. So it will depend on the amount of thrust delivered and the low speed drag curve of the aircraft. In other words Vx will not be a fixed multiple of Vs. If one had to generalize across the GA fleet, I would guess that 1.2 to 1.3 Vs would usually be close. As always, when diving into performance problems, I stand ready to learn from a better (or more accurate!) answer. Fire away!
Best regards,
Westhawk