Convolutional neural network (CNN) has been widely applied in hyperspectral image (HSI) classification exhibiting excellent performance. Weak generalization of CNN models to different datasets is a common issue in this domain largely because of limited amount of labeled training samples. In this article, we propose a shape fully group convolutional neural network (FGCNN) method that integrates cascades of shuffled group convolutions tailored to different network stages. To our knowledge, this is the first reported full-group CNN model in general, and we design it in particular for robust spectral-spatial classification of HSI. In the primary feature extraction stage, we develop an original multiscale spectral feature extraction approach based on a novel concept of multi-kernel depthwise convolution that we define in terms of shuffled and importance-weighted group convolution. In the subsequent stage, we introduce a discriminative spectral-spatial feature extraction method with a novel group competition block to capture informative features with relatively few parameters. The final feature fusion stage is defined as a novel lightweight group feature fusion method that sharply reduces fusion weights compared to traditional methods with fully connected layers. Experimental results on three datasets show that the proposed FGCNN yields robust classification accuracy under the same hyperparameter settings compared to the current state-of-the-art.