Recent improvements in generative adversarial visual synthesis incorporate real and fake image transformation in a self-supervised setting, leading to increased stability and perceptual fidelity. However, these approaches typically involve image augmentations via additional regularizers in the GAN objective and thus spend valuable network capacity towards approximating transformation equivariance instead of their desired task. In this work, we explicitly incorporate inductive symmetry priors into the network architectures via group-equivariant convolutional networks. Group-convolutions have higher expressive power with fewer samples and lead to better gradient feedback between generator and discriminator. Further, group-representations are especially relevant for modalities such as medical imaging, where image labels are typically invariant under rotation/reflection. We show that group-equivariance integrates seamlessly with recent techniques for GAN training across regularizers, architectures, and loss functions. We demonstrate the utility of our methods for conditional synthesis by improving generation in the limited data regime across globally-symmetric imaging datasets and even finding benefits for natural images with preferred orientation.