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The relation between the monopole transition strength and existence ofcluster structure in the excited states is discussed based on an algebraiccluster model. The structure of $^{12}$C is studied with a 3$\alpha$ model, andthe wave function for the relative motions between $\alpha$ clusters aredescribed by the symplectic algebra $Sp(2,R)_z$, which corresponds to thelinear combinations of $SU(3)$ states with different multiplicities.Introducing $Sp(2,R)_z$ algebra works well for reducing the number of the basisstates, and it is also shown that states connected by the strong monopoletransition are classified by a quantum number $\Lambda$ of the $Sp(2,R)_z$algebra.

Symplectic structure and monopole strength in 12C