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