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The Lie algebra stabilizers of the forms from Table 1 can easily be computed by solving the linear equation for . They are explicitly given below as linear subspaces of .

The commutator subalgebra is perfect of dimension 3. The radical of equals its center and is .

This Lie algebra is solvable. has dimension 2. Its center is 2-dimensional; its nilpotent radical is 4-dimensional.

The commutator subalgebra is abelian of dimension 3 and so is solvable. Its center is . Its nilpotent radical is 4-dimensional.

This Lie algebra is solvable. Its nilpotent radical is 4-dimensional. Its center is .

The solvable radical of this Lie algebra is 7-dimensional. There is a 3-dimensional Levi subalgebra. The center is .

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