We studied the background dwarf nova of KIC 11412044 in the Kepler public data and identified it with GALEX J194419.33 + 491257.0 . This object turned out to be a very active SU UMa-type dwarf nova having a mean supercycle of about 150 d and frequent normal outbursts having intervals of 4–10 d. The object showed strong persistent signal of the orbital variation with a period of 0.0528164 ( 4 ) d ( 76.06 min ) and superhumps with a typical period of 0.0548 d during superoutbursts . Most of the superoutbursts were accompanied by a precursor outburst . All these features are unusual for this very short orbital period . We succeeded in detecting the evolving stage of superhumps ( stage A superhumps ) and obtained a mass ratio of 0.141 ( 2 ) , which is unusually high for this orbital period . We suggest that the unusual outburst properties are a result of this high mass ratio . We suspect that this object is a member of the recently recognized class of cataclysmic variables ( CVs ) with a stripped core evolved secondary which are evolving toward AM CVn-type CVs . The present determination of the mass ratio using stage A superhumps makes the first case in such systems .