64% n.th + COP4 = more heat out of fuel than its calorific value?

[cmb]

TL;DR

If a CCGT generates electrical power at 64% efficiency, and a heat pump generates 4 times the thermal power to electrical power, is that more heat energy out than the fuel has?

Something that has been on my mind a while.

If a CCGT generates electrical power at 64% efficiency, and a COP4 heat pump, powered by that generator, generates 4 times the thermal power to electrical power, wouldn't that mean we can get 256% heat out of the fuel's calorific value?

Maybe that is OK, but seems non-intuitive.

Where does the extra heat come from, or what am I not understanding?

I presume the answer is that because we're going from 'very hot' heat to colder heat, we can suck up some of the environmental heat? If so, is there not a more direct way to use the combustion temperature from a burning fuel to directly suck in extra heat from the environment, missing out the electrical generation bit?

 

[Lnewqban]

Please, see:
https://www.carrier.com/residential/en/us/products/heat-pumps/heat-pump-efficiency/

 

[russ_watters]

Short summary of @Llewelyn 's point: COP is like efficiency, but it is not efficiency. It is always way over 100%. That's not a violation of the laws of thermo. The energy isn't being created, just moved, and there are hard restrictions on the available temperature deltas.