A possible form of the Lipkin model obeying the su(6)-algebra is presented. It is a natural generalization from the idea for the su(4)-algebra recently proposed by the present authors. All the relation appearing in the present form can be expressed in terms of the spherical tensors in the su(2)-algebras. For specifying the linearly independent basis completely, twenty parameters are introduced. It is concluded that, in these parameters, the ten denote the quantum numbers coming from the eigenvalues of some hermitian operators. The five in these ten determine the minimum weight state.
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