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A group code is a set of vectors, generated by a group of orthogonal matrices transforming a starting vector. Ingemarsson  has shown that, if the group is commutative, the code is equivalent to a set of phase-modulated signals. Codes generated by noncommutative groups have been described by Slepian . In this paper another class of codes generated by noncommutative groups is described. This class is called group codes for PHAMP signals and can be described as a combination of phase- and amplitude-modulated signals. The performance of these codes, when communicating over the Gaussian channel, is analyzed, and it is shown that some of them have a performance close to the bounds given by Slepian .