Group theory is a sort of strong mathematics tool for the researches of the symmetry property. Chaos is the internal randomicity put up by the definite non-linear dynamical system. It has several properties, including the limitary, the nonperiodic and the dependence on initial condition and parameters. The discrete sequences produced by chaos system are often used to encrypt data such as digital pictures. In former papers, the relationship of Group theory and Chaotic system has seldom been studied. In this paper, it proves the result that the scrambling transform of two-dimensional chaotic scrambling arrays will form permutation groups. It is proposed on the basic theory of Group and Chaos and is proved in theoretical and experiment ways. According to the result, it is demonstrated invalid to use two-dimensional chaotic scrambling arrays created by different chaotic system and different initial values to encrypt multimedia data such as digital images and videos.