We present a design of graded-index ring-core fiber (GI-RCF) supporting 3 linearly polarized (LP) mode-groups (i.e. LP01, LP11 and LP21) with a single radial index of one for mode-division multiplexed (MDM) transmission. Reconfigurable spatial light modulator (SLM) based spatial (mode) (de)multiplexers are used to systematically characterize spatial/temporal modal properties of the GI-RCF. We also demonstrate all-optical mode-group multiplexed transmissions over a 360m fabricated GI-RCF without using multiple-input multiple-output digital signal processing (MIMO DSP).The UK Engineering and Physical Sciences Research Council (EPSRC) grant: EP/J009369/1 (COMIMO); a Cambridge University EPSRC Impact Acceleration Account (IAA) follow-on grant