Levi-Civita Tensor & Group Theory: Symmetry?

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

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