We demonstrate a record-long 10-mode-multiplexed transmission over 1300 km using a 6-LP few-mode fiber (FMF). Long-haul mode-division-multiplexed (MDM) transmission systems face challenges posed by the pulse broadening effect caused by differential mode delay (DMD), which hampers performance and increases computational complexity for receiver-side multiple-input multiple-output digital signal processing (MIMO-DSP) to mitigate mode mixing effects. In this study, we extend the application of mode permutation techniques, specifically the cyclic mode-group permutation (CMGP), as a solution to address these performance limitations in 10-spatial-mode-multiplexed long-haul transmission. We present experimental results conducted over a 6-LP graded-index (GI) FMF, demonstrating the effectiveness of CMGP in improving spatial channel coupling and reducing pulse spreading with comparisons with several CMGPadopted configurations. The introduction of CMGP realized a modal-dispersion-unmanaged link, even when employing a 6-LP FMF with a modal dispersion coefficient of 157 ps/km, achieving the world's longest 1300-km transmission utilizing 10 spatial modes while reducing the impact of the modal dispersion accumulation by 82 % Index Terms-Space division multiplexing (SDM), Mode division multiplexing (MDM), Differential modal dispersion (DMD), Cyclic mode-group permutation (CMGP)