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.
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