It should state the gallons per minute on a label attached to the pump, or on the pump maker's website. To experiment yourself, would involve pumping a measured number of gallons using a stop watch!
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That will also depend on how high the water is to be pumped: to pump it higher requires more energy per second, i.e., more power.
The pool is 4ft*23ft*11ft = 1012 cubic feet You can pump in 8.2 cubic feet every minute. So time taken to fill it = 1012/8.2 = 123.4 minutes = 2 hours, 3.4 minutes.
254 GPM
Each pump is different, but you should get somewhere about 6000 gph
I would recommend 1 HP