mp.mathematical physics - The bosonic and fermionic parts of the orthosymplectic super Lie-Algebra

The way I would understand it that $osp(6,2|4)$ is the group of linear tansformations
of a real super vector space with a non-degenerate symmetric inner product. The even (bosonic) vector space has dimension 8 and the inner product is symmetric with signature
$(6,2)$ the odd (fermionic) part has dimension 4 and a symplectic form.

The even part is then the product of the groups of these two vector spaces, namely $o(6,2)$ and $sp(4)$. There is an isomophism of rank two Lie algebras $sp(4)cong so(5)$; to see this note that the spin representation has dimension 4 and has an invariant symplectic form.

I realise you have $so(5,1)$ where I have $so(6,2)$. I don't know what is going on here but $so(6,2)$ is the group of conformal transformations of $R^{5,1}$.