The structure constant $f_{abc}$ of Lie group is defined by the commutators of generators,
$$[T^a,T^b]=i f_{abc}T_c$$
automatically $f_{abc}=-f_{bac}$.
Can someone give a list of explicit examples of Lie groups such that the structure constant with the property:
$$f_{abc} \neq f_{bca}$$
(i.e. not cyclic.)
The more examples the better. Thank you.
(ps.For $f_{abc} =f_{bca}$, the Lie group has to be compact semi-simple(?).)