Spin8 blocks Block Sizes in Compact Inner Class: PSO(8) PSO(6,2) PSO*(8)+ PSO*(8)- PSO(4,4) Spin(8) 0 0 0 0 1 Spin(6,2) 0 6 0 0 38 Spin*(8)+ 0 0 6 0 38 Spin*(8)- 0 0 0 6 38 Spin(4,4) 1 28 28 28 111 Block Sizes in Unequal Rank Inner Class: PSO(7,1) PSO(5,3) Spin(7,1) 0 4 Spin(5,3) 4 48