http://superstringtheory.com/basics/basic5a.html
this should answer your questions. The basic principle is how the certain modes of the one dimensional string behave under the group symmetries such as E(8)xE(8) which allows us to identify how the different modes of the string behave as...
Because there is a finite amount of groups and the bigger they get the more symmetries they contain. They usually look at SO(p,q) bigger than S0(3,1) in spatial dimensions because the conformal group doesn't have enough symmetry hence moving to a bigger rotation group will allow for more...