The question asked Cartan - is "What is the symmetry group octonions?". If you - a Cartan, the answer to this question you know. Octonions symmetry group is the smallest of the exceptional simple Lie groups - one that is known as the G2. 8-dimensional system octonions has a 14-dimensional symmetry group. Exceptional normed division algebra is directly related to the first of the exceptional Lie groups. To move forward, we need to make friends with a single idea, which goes back to the Renaissance - but not to the mathematicians and the artists of the time.