Modern combined cycle gas turbines offer thermal-to-electric efficiency over 60% (on a lower heating value fuel basis) at full design load, e.g. this General Electric system at 64%:

https://www.ge.com/news/press-releases/ha-technology-now-ava...

Approximating natural gas as 100% methane, that means the thermal-to-electric efficiency on a higher heating value basis is more like 57-58%:

https://en.wikipedia.org/wiki/Heat_of_combustion#Heat_of_com...

But neither of these efficiency measures account for district heating with waste heat.