Conjugacy classes of Cartan subgroups for the simply connected split group of type G2 Cartan #0: split: 2; compact: 0; complex: 0 imaginary root system is empty real root system: G2 complex factor is empty twisted involution orbit size: 12/12 = 1 size of parameter space fiber: 1.4 = 4 Cartan #1: split: 0; compact: 0; complex: 1 imaginary root system: A1 real root system: A1 complex factor is empty twisted involution orbit size: 12/4 = 3 size of parameter space fiber: 1.1 = 1 Cartan #2: split: 0; compact: 0; complex: 1 imaginary root system: A1 real root system: A1 complex factor is empty twisted involution orbit size: 12/4 = 3 size of parameter space fiber: 1.1 = 1 Cartan #3: split: 0; compact: 2; complex: 0 imaginary root system: G2 real root system is empty complex factor is empty twisted involution orbit size: 12/12 = 1 size of parameter space fiber: 4.1 = 4 total number of parameters for this inner class: 4 + 3 + 3 + 4 = 14