Your transistor probably does not have any negative feedback so it will be extremely distorted at high output levels even if it is not clipping.
If its load is 60k ohms or more then its voltage gain is about 120 but the severe distortion will make it difficult to measure.
There are three capacitors and the one across the emitter resistor has a high value so I think there is no negative feedback. Just high gain and distortion.
There are many articles that say the hfe or hFE does not affect a transistor's voltage gain.
The first article in Google is from Amature Radio magazine: THE TRANSISTOR AS A VOLTAGE AMPLIFIER
It is the angle of the slope of the base voltage to the collector voltage that shows the voltage gain of a common emitter transistor. When the hfe is high then the slope stays the same but it shifts downward. When the hfe is low then the slope stays the same but shifts upwards.
It is the angle of the slope of the base voltage to the collector voltage that shows the voltage gain of a common emitter transistor. When the hfe is high then the slope stays the same but it shifts downward. When the hfe is low then the slope stays the same but shifts upwards.
There are many articles that say the hfe or hFE does not affect a transistor's voltage gain.
The first article in Google is from Amature Radio magazine: THE TRANSISTOR AS A VOLTAGE AMPLIFIER
The author of this article makes a small error just above Figure 2. He says:
"Base current equals collector current (or emitter current) divided by Hfe and hence, with near constant voltage across the base/emitter forward biased junction, input resistance (Rb) is multiplied by Hfe. Thus we get:"
Actually, base current equals collector current divided by Hfe, or emitter current divided by (Hfe+1), but not emitter current divided by Hfe.
This means that the input resistance seen at the base of a common emitter amplifier with no (or bypassed) external emitter resistance is .026/Ie * (Hfe+1), not .026/Ie * Hfe.
So his gain expression needs to be multiplied by Hfe/(Hfe+1), and the gain of a common emitter amplifier does depend on Hfe. The dependence is slight, and becomes completely negligible for reasonably high values of Hfe, but the slight dependence is really there.
.... the gain of a common emitter amplifier does depend on Hfe. The dependence is slight, and becomes completely negligible for reasonably high values of Hfe, but the slight dependence is really there.
Exactly. This is the case for a stand-alone single common emitter stage driven by a low impedance source.
However, the author of that piece does make the point that a much greater effect is the decreased loading on a previous, moderate-to-high output impedance stage, as hfe increases.
The distortion from a common-emitter amplifier transistor that has no negative feedback, at a fairly high output level and driven from a low impedance source is so high that it is difficult to measure its gain:
It's not that difficult. Just reduce the input to 1 mV or less as appropriate. Such a high gain stage would only be used to amplify very small signals anyway.