It follows from the classification that any p -compact group can be written as BG = BH × BK where BH is the p -completion of a compact connected Lie group and BK is finite direct product of simple exotic p-compact groups i.e., simple p-compact groups whose Weyl group group is not a Z -reflection groups. Simple exotic p-compact groups are again in 1-1-correspondence with irreducible complex reflection groups whose character field can be embedded in Q p , but is not Q .