We propose a novel feature coding method that exploits invariance. We consider the setting where the transformations that preserve the image contents compose a finite group of orthogonal matrices. This is the case in many image transformations, such as image rotations and image flipping. We prove that the group-invariant feature vector contains sufficient discriminative information when learning a linear classifier using convex loss minimization. From this result, we propose a novel feature modeling for principal component analysis and k-means clustering, which are used for most feature coding methods, and global feature functions that explicitly consider the group action. Although the global feature functions are complex nonlinear functions in general, we can calculate the group action on this space easily by constructing the functions as the tensor product representations of basic representations, resulting in the explicit form of invariant feature functions. We demonstrate the effectiveness of our methods on several image datasets.