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It is proved that there is no chaotic group actions on any topological space with free arc.In this paper the chaotic actions of the group like G×F,where F is a finite group,are studied.In particular,under a suitable assumption,if F is a cyclic group,then the topological space which admits a chaotic action of Z×F must admit a chaotic homeomorphism.A topological space which admits a chaotic group action but admits no chaotic homeomorphism is constructed.