Majorana representation of A 6 involving 3C-algebras

We study a possible Majorana representation ${{\mathcal R}}$ of the alternating group A 6 of degree 6 such that for some involutions s and t in A 6, generating a D 6-subgroup, the corresponding Majorana axes a s and a t generate a subalgebra of type 3C. We show that there exists at most one such representation ${{\mathcal R}}$ and that its dimension is at most 70. The representation ${{\mathcal R}}$ does not correspond to a subalgebra in the Monster algebra generated by a subset of the Majorana axes canonically indexed by the involutions of an A 6-subgroup in the Monster.