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C130s were designed to operate from relatively short unimproved runways. If the place has enough runway to operate corporate jets, it should have enough for a C130.
EDIT: This place only has enough runway (2998 x 50 ft ) for small Cessna size aircraft, so no jets or C130s.
I reckon a C130 could use it actually. The US Navy landed one on a carrier, which is probably shorter then this runway.
Edit: yes, USS Nimitz is 1/3 the length of this runway. C130 could land and take-off there with no issues.