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A seven-core few-mode multicore fiber in which each core supports both the LP01 mode and the two degenerate LP11 modes has been designed and fabricated for the first time, to the best of our knowledge. The hole-assisted structure enables low inter-core crosstalk and high mode density at the same time. LP01 inter-core crosstalk has been measured to be lower than -60 dB/km. LP11 inter-core crosstalk has been measured to be around -40 dB/km using a different setup. The LP11 free-space excitation-induced crosstalk is simulated and analyzed. This fiber allows multiplexed transmission of 21 spatial modes per polarization per wavelength. Data transmission in LP01/LP11 mode over 1 km of this fiber has been demonstrated with negligible penalty.