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We present results from multiwavelength observations of the BL Lacertae object 1ES 1741 + 196, including results in the very high energy gamma-ray regime using the Very Energetic Radiation Imaging Telescope Array System (VERITAS). The VERITAS time-averaged spectrum, measured above 180 GeV, is well modelled by a power law with a spectral index of 2.7 +/- 0.7(stat) +/- 0.2(syst). The integral flux above 180 GeV is (3.9 +/- 0.8(stat) +/- 1.0(syst)) x 10(-8) m(-2) s(-1), corresponding to 1.6 per cent of the Crab nebula flux on average. The multiwavelength spectral energy distribution of the source suggests that 1ES 1741+196 is an extreme-high-frequency-peaked BL Lacertae object. The observations analysed in this paper extend over a period of six years, during which time no strong flares were observed in any band. This analysis is therefore one of the few characterizations of a blazar in a non-flaring state.