Dimensions of $E_{7\frac{1}{2}}$

Is there much known about the dimensions $ D$ of $ E_{7\frac{1}{2}}$ ($ D_6.H_{32}$ ) beyond $ 44\bigotimes44(def)=1\bigoplus945\bigoplus99(adj)\bigoplus891$ ? Generally, does a weight indexing scheme like for the semisimple $ E_7$ cousins exist? Particularly, is $ D=134805$ an irrep dimension or the sum of two $ D_1+D_2$ ? Background: In the $ E_7$ series, in $ def^{\bigotimes4}$ there always pops up a pair of dimensions with equal quadratic Casimir ($ C=6(m+1)$ , your gauge may vary, I conform to the Hayashi paper on quantum dimensions) but in most cases one partner will be identically zero (one example for each case: $ E_7,m=8,C=54,D_1=365750,D_2=0;C_3,m=1,C=12,D_1=525,D_2=385$ ). And my “magic” formulae only give the sum.
P.S. In case nothing is known and anyone needs a few dimensions $ D$ of $ E_{7\frac{1}{2}}$ together with the quadratic casimirs and the Clebsch-Gordan series, just ask – what I do is not math but it works 🙂