Conjugacy classes of Cartan subgroups for the adjoint quasisplit group of type E6 Cartan #0: split: 2; compact: 0; complex: 2 imaginary root system is empty real root system: D4 complex factor: A2 twisted involution orbit size: 51840/1152 = 45 size of parameter space fiber: 1.4 = 4 Cartan #1: split: 0; compact: 0; complex: 3 imaginary root system: A1 real root system: A1.A1.A1 complex factor: A2 twisted involution orbit size: 51840/96 = 540 size of parameter space fiber: 1.1 = 1 Cartan #2: split: 0; compact: 2; complex: 2 imaginary root system: A3 real root system: A1.A1 complex factor: A1 twisted involution orbit size: 51840/192 = 270 size of parameter space fiber: 4.1 = 4 Cartan #3: split: 0; compact: 4; complex: 1 imaginary root system: A5 real root system: A1 complex factor is empty twisted involution orbit size: 51840/1440 = 36 size of parameter space fiber: 16.1 = 16 Cartan #4: split: 0; compact: 6; complex: 0 imaginary root system: E6 real root system is empty complex factor is empty twisted involution orbit size: 51840/51840 = 1 size of parameter space fiber: 64.1 = 64 total number of parameters for this inner class: 180 + 540 + 1080 + 576 + 64 = 2440