Levi-Civita Tensor & Group Theory: Symmetry?

[nateHI]

I have been trying to think about the Levi-Civita tensor in the context of Group Theory. Is there a group that it is symmetric to?

I'm sorry if this is a double post but I don't think my original identical post submitted correctly.

Thanks, Nate

 

[LagrangeEuler]

You mean under the composition of Levi Civita?
For example $\epsilon_{ijk}\cdot \epsilon_{lmn}$. Well I'm not sure.

 

[ChrisVer]

Since the Levi Civita symbol is subject to permutations, i think that it has to do with a Symmetric group...
(it's a guess if someone knows for sure I'd be happy to see it).