The cyclic group of order 12 acts on {1,2,..., 12} with the following cycle structure. (1) (**)(**)(**)(**)(**)(**) 1× ***)(* **)(***)(***) 2 × (****)(****)(****) (******)(******) (************) 1 x 2 x 2 x 4 x Determine the number of different colored necklaces with 12 beads when each bead is colored with one of 3 colors.

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