#This is the real group of type E6, with maximal compact F4 #The Weyl group of the fundamental Cartan (which is not compact) if #of type F4. This shows W(F4)=W(A2) semidirect W(D4) This is the Atlas of Reductive Lie Groups Software Package version 0.2.3. Enter "help" if you need assistance. empty: type Lie type: E6 elements of finite order in the center of the simply connected group: Z/3 enter kernel generators, one per line (ad for adjoint, ? to abort): sc enter inner class(es): s main: realweyl (weak) real forms are: 0: e6(f4) 1: e6(R) enter your choice: 0 there is a unique conjugacy class of Cartan subgroups Name an output file (hit return for stdout): real weyl group is W^C.((A.W_ic) x W^R), where: W^C is isomorphic to a Weyl group of type A2 A is trivial W_ic is a Weyl group of type D4 W^R is trivial generators for W^C: 35 16 generators for W_ic: 34543 4 2 134565431