I am assuming you are using this as part of a permanent installation, not an extension cord. It is not appropriate for an extension cord.
Stranded equipment grounding counductor or solid makes no difference. The purpose of the equipment grounding conductor is to carry enough current to trip the breaker in case of a ground fault. Only the gauge matters.
FWIW according to the NEC the ampacity of 6 ga. wire in a cable like this is 65 amps when everything including the panel, cable, breakers, receptacles, etc. are rated for 75 degrees C, but only 55 amps if any component is only rated only for 60 degrees C. And of course, this is before any reduction for operation in an ambient temperature of over 86 degrees F.