The growth of fingerprint databases creates a need for strategies to reduce the identification time. Fingerprint classification reduces the search penetration rate by grouping the fingerprints into several classes. Typically, features describing the visual patterns of a fingerprint are extracted and fed to a classifier. The extraction can be time-consuming and error-prone, especially for fingerprints whose visual classification is dubious, and often includes a criterion to reject ambiguous fingerprints. In this paper, we propose to improve on this manually designed process by using deep neural networks, which extract implicit features directly from the images and perform the classification within a single learning process. An extensive experimental study assesses that convolutional neural networks outperform all other tested approaches by achieving a very high accuracy with no rejection. Moreover, multiple copies of the same fingerprint are consistently classified. The runtime of convolutional networks is also lower than that of combining feature extraction procedures with classification algorithms.