Conjugacy classes of Cartan subgroups for the simply connected split group of type E7 Cartan #0: split: 7; compact: 0; complex: 0 imaginary root system is empty real root system: E7 complex factor is empty twisted involution orbit size: 2903040/2903040 = 1 size of parameter space fiber: 1.128 = 128 Cartan #1: split: 5; compact: 0; complex: 1 imaginary root system: A1 real root system: D6 complex factor is empty twisted involution orbit size: 2903040/46080 = 63 size of parameter space fiber: 1.32 = 32 Cartan #2: split: 3; compact: 0; complex: 2 imaginary root system: A1.A1 real root system: D4.A1 complex factor: A1 twisted involution orbit size: 2903040/3072 = 945 size of parameter space fiber: 1.8 = 8 Cartan #3: split: 1; compact: 0; complex: 3 imaginary root system: A1.A1.A1 real root system: A1.A1.A1.A1 complex factor: A2 twisted involution orbit size: 2903040/768 = 3780 size of parameter space fiber: 1.2 = 2 Cartan #4: split: 2; compact: 1; complex: 2 imaginary root system: A1.A1.A1 real root system: D4 complex factor: A2 twisted involution orbit size: 2903040/9216 = 315 size of parameter space fiber: 4.4 = 16 Cartan #5: split: 1; compact: 2; complex: 2 imaginary root system: D4 real root system: A1.A1.A1 complex factor: A2 twisted involution orbit size: 2903040/9216 = 315 size of parameter space fiber: 4.2 = 8 Cartan #6: split: 0; compact: 1; complex: 3 imaginary root system: A1.A1.A1.A1 real root system: A1.A1.A1 complex factor: A2 twisted involution orbit size: 2903040/768 = 3780 size of parameter space fiber: 4.1 = 4 Cartan #7: split: 0; compact: 3; complex: 2 imaginary root system: D4.A1 real root system: A1.A1 complex factor: A1 twisted involution orbit size: 2903040/3072 = 945 size of parameter space fiber: 16.1 = 16 Cartan #8: split: 0; compact: 5; complex: 1 imaginary root system: D6 real root system: A1 complex factor is empty twisted involution orbit size: 2903040/46080 = 63 size of parameter space fiber: 64.1 = 64 Cartan #9: split: 0; compact: 7; complex: 0 imaginary root system: E7 real root system is empty complex factor is empty twisted involution orbit size: 2903040/2903040 = 1 size of parameter space fiber: 256.1 = 256 total number of parameters for this inner class: 128 + 2016 + 7560 + 7560 + 5040 + 2520 + 15120 + 15120 + 4032 + 256 = 59352