Even without auxiliary images, single hyperspectral image super-resolution (SHSR) methods can be designed to improve the spatial resolution of hyperspectral images. However, failing to explore coherence thoroughly along bands and spatial-spectral information leads to the limited performance of the SHSR. In this study, we propose a novel group-based SHSR method termed the efficient feedback gate network, which uses various feedbacks and gate operations involving large kernel convolutions and spectral interactions. In particular, by providing different guidance for neighboring groups, we can learn rich band information and hierarchical hyperspectral spatial information using channel shuffling and dilatation convolution in shuffled and progressive dilated fusion module(SPDFM). Moreover, we develop a wide-bound perception gate block and a spectrum enhancement gate block to construct the spatial-spectral reinforcement gate module (SSRGM) and obtain highly representative spatial-spectral features efficiently. Additionally, we apply a three-dimensional SSRGM to enhance holistic information and coherence for hyperspectral data. The experimental results on three hyperspectral datasets demonstrate the superior performance of the proposed network over the state-of-the-art methods in terms of spectral fidelity and spatial content reconstruction.