The symplectic group $\text{Sp}(2n)$ is defined in terms of the set of $2n$ by $2n$ complex matrices that preserve a bilinear form:
$$\text{Sp}(2n) = \{M \in M_{2n \times 2n}(\mathbb{C}) : M^T \Omega M = \Omega \}\text{ where } \Omega = \begin{pmatrix} 0 & I_n \\ -I_n & 0 \end{pmatrix}$$
By introducing a $2\times 2$ Levi-Civita tensor $\epsilon_{ij} = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$ and an $n \times n$ Kronecker delta $\delta_{ij}$ (here $i$ runs from $1$ to $n$), we can rewrite this definition in Einstein summation notation as:
$$\text{Sp}(2n) = \{M \in M_{2n \times 2n}(\mathbb{C}) : M_{ik,mo} M_{jl,np} \epsilon_{mn} \delta_{op} = \epsilon_{ij} \delta_{kl} \}$$
However, we can ask what happens when we instead consider higher-dimensional Levi-Civita tensors and Kronecker deltas.
For example, we can consider a $3\times 3 \times 3$ Levi-Civita $\epsilon^{ijk}$ which is the completely antisymmetric tensor on three indices. We can consider an $n \times n \times n$ Kronecker delta $\delta_{ijk}$ which is one if $i=j=k$ and zero otherwise.
This allows me to define a new mystery set
$$\text{G}(3n) = \{M \in M_{3n \times 3n}(\mathbb{C}) : M_{il,ps} M_{jm,qt} M_{kn,ru} \epsilon_{pqr} \delta_{stu} = \epsilon_{ijk} \delta_{lmn} \}$$
I view this set $\text{G}(3n)$ as a generalization of the symplectic group above, but I'm not sure what properties it might inherit. I'm unfamiliar with the finer details of defining groups or sets in terms of trilinear invariants like the above.
To make my question concrete, does this set $\text{G}(3n)$ correspond to some well-known group? Does the intersection of this set with the set of $3n\times 3n$ unitary matrices correspond to some well-known group?