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This gun could be in either .177 or .22 cal but its low power means it's not suitable for shooting vermin, except perhaps at very close ranges. The Beeman blue book gives the Series 70 Mod 77's velocity at just 400fps for .177 and 300 for .22, which is the equivalent of a not especially powerful air pistol and they are nowadays considered unsuitable for vermin shooting.
Maybe Beeman is mistaken (it wouldn't be the first time) so perhaps you'd better have the power checked on a chronograph before you contemplate hunting with it. Someone more knowledgable about hunting with low-powered guns will be along in a minute.