C, D♭, F, G♭, A♭, B♮.
Does a scale using the notes above exist? Here is what is looks on a sheet:
A one Mr. Ian Ring has a whole website devoted to the categorization and study of every possible scale. I suggest you check it out; it contains a veritable treasure trove of information on just about any scale you can imagine. From Ring's website, Zeitler called this scale "Lycrimic". Of course, this scale is obscure enough that a search under that name pretty much only turns up websites devoted to listing all scales - you can call it whatever you want without fear of correction!