A CCD photometry of the dwarf nova MASTER OT J172758.09 +380021.5 was carried out in 2019 during 134 nights. Observations covered three superoutbursts, five normal outbursts and quiescence between them. The available ASASSN and ZTF data for 2014-2020 were also examined. Spectral observations were done in 2020 when the object was in quiescence. Spectra and photometry revealed that the star is an H-rich active ER UMa-type dwarf nova with a highly variable supercycle of ~50-100 d that implies a high and variable mass-transfer rate. This object demonstrated peculiar behaviour: short-lasted superoutbursts (a week); a slow superoutburst decline and cases of rebrightenings; low frequency (from none to a few) of the normal outbursts during the supercycle. In 2019 a mean period of positive superhumps was found to be 0.05829 d during the superoutbursts. Late superhumps with a mean period of 0.057915 d which lasted about ~20 d after the end of superoutburst and were replaced by an orbital period of 0.057026 d or its orbital-negative superhump beat period were detected. An absence of eclipse in the orbital light curve and its moderate amplitude are consistent with the orbital inclination of about 40 degr found from spectroscopy. The blue peaks of the V-Ic and B-Rc of superhumps during the superoutburst coincided with minima of the light curves, while B-Rc of the late superhumps coincided with a rising branch of the light curves. We found that a low mass ratio q=0.08 could explain most of the peculiarities of this dwarf nova. The mass-transfer rate should be accordingly higher than what is expected from gravitational radiation only, this assumes the object is in a post-nova state and underwent a nova eruption relatively recently -- hundreds of years ago. This object would provide probably the first observational evidence that a nova eruption can occur even in CVs near the period minimum.
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