Itisprovedthatthereisnochaoticgroupactionsonanytopologicalspacewithfreearc.InthispaperthechaoticactionsofthegrouplikeG×F,whereFisafinitegroup,arestudied.Inparticular,underasuitableassumption,ifFisacyclicgroup,thenthetopologicalspacewhichadmitsachaoticactionofZ×Fmustadmitachatotichomeomorphism.Atopologicalspacewhichadmitsachaoticgroupactionbutadmitsnochaotichorneomorphismisconstructed.
