SU(3) needs to act on a minumum of 4 compact dimensions. SU(2) needs a minimum of 2 dimensions U(1) needs a minumum of 1 dimension Thus SU(3)xSU(2)xU(1) needs 7 extra dimensions. Because of this, string theoretists do not use the extra dimensions to generate the gauge groups, and they use instead -wrongly, IMO- the flavour group of the superstring, because in string theory it is a local gauge group too. Note that if SU(2) were wiped out, we would need only 5 extra dimensions. Now, the standard model is not SU(3)xSU(2)xU(1), not SU(3)xU(1), but something between: the electroweak symmetry is broken but not deleted. Question is: does the breaking of the group make room to use a dimension lower than seven? In this view, in the limit were the Higgs goes to zero symmetry is restored and the dimension should be seven (or 11, if you wish to count spacetime). But with the Higgs around, we could be using a dimension less than seven. Intriguingly, Connes and Chamseddine concluded, in the 2006, that the dimension of the finite part of the standard model spectral triple was 6 (mod 8). And the CC model is forced to incorporate the Higgs automagically.