Tolerance to image variations (e.g. translation, scale, pose, illumination) is an important desired property of any object recognition system, be it human or machine. Moving towards increasingly bigger datasets has been trending in computer vision specially with the emergence of highly popular deep learning models. While being very useful for learning invariance to object inter- and intra-class shape variability, these large-scale wild datasets are not very useful for learning invariance to other parameters forcing researchers to resort to other tricks for training a model. In this work, we introduce a large-scale synthetic dataset, which is freely and publicly available, and use it to answer several fundamental questions regarding invariance and selectivity properties of convolutional neural networks. Our dataset contains two parts: a) objects shot on a turntable: 16 categories, 8 rotation angles, 11 cameras on a semicircular arch, 5 lighting conditions, 3 focus levels, variety of backgrounds (23.4 per instance) generating 1320 images per instance (over 20 million images in total), and b) scenes: in which a robot arm takes pictures of objects on a 1:160 scale scene. We study: 1) invariance and selectivity of different CNN layers, 2) knowledge transfer from one object category to another, 3) systematic or random sampling of images to build a train set, 4) domain adaptation from synthetic to natural scenes, and 5) order of knowledge delivery to CNNs. We also explore how our analyses can lead the field to develop more efficient CNNs.