Cognitive radios sense the radio spectrum in order to find unused frequency bands and use them in an agile manner. Transmission by the primary user must be detected reliably even in the low signal-to-noise ratio (SNR) regime and in the face of shadowing and fading. Communication signals are typically cyclostationary, and have many periodic statistical properties related to the symbol rate, the coding and modulation schemes as well as the guard periods, for example. These properties can be exploited in designing a detector, and for distinguishing between the primary and secondary users' signals. In this paper, a generalized likelihood ratio test (GLRT) for detecting the presence of cyclostationarity using multiple cyclic frequencies is proposed. Distributed decision making is employed by combining the quantized local test statistics from many secondary users. User cooperation allows for mitigating the effects of shadowing and provides a larger footprint for the cognitive radio system. Simulation examples demonstrate the resulting performance gains in the low SNR regime and the benefits of cooperative detection.