Cartan #0:
split: 0; compact: 7; complex: 0
canonical twisted involution: e
twisted involution orbit size: 1; fiber size: 128; strong inv: 128
imaginary root system: D7
real root system is empty
complex factor is empty
real form #4: [0,1,2,4,5,6,8,10,11,13,16,17,18,20,21,22,24,26,27,29,96,98,99,
    101,104,105,106,108,109,110,113,116,118,119,123] (35)
real form #3: [3,7,9,12,14,19,23,25,28,30,97,100,102,107,111,112,114,117,120,
    122,125] (21)
real form #1: [15,31,103,115,121,124,126] (7)
real form #2: [32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,
    53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,
    78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95] (64)
real form #0: [127] (1)


Cartan #1:
split: 0; compact: 5; complex: 1
canonical twisted involution: 2,3,4,5,6,7,5,4,3,2,1,2,3,4,5,6,7,5,4,3,2
twisted involution orbit size: 42; fiber size: 32; strong inv: 1344
imaginary root system: A1.D5
real root system: A1
complex factor is empty
real form #4: [0,2,4,8,10,12,16,20,22,26] (10)
real form #2: [1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31] (16)
real form #3: [6,14,18,24,28] (5)
real form #1: [30] (1)


Cartan #2:
split: 2; compact: 5; complex: 0
canonical twisted involution: 1,2,3,4,5,6,7,5,4,3,2,1
twisted involution orbit size: 21; fiber size: 32; strong inv: 672
imaginary root system: D5
real root system: A1.A1
complex factor: A1
real form #4: [0,1,2,4,5,6,8,10,11,13] (10)
real form #3: [3,7,9,12,14] (5)
real form #1: [15] (1)


Cartan #3:
split: 0; compact: 3; complex: 2
canonical twisted involution: 4,5,6,7,5,4,3,4,5,6,7,5,4,2,3,4,5,6,7,5,4,1,2,3,4,
    5,6,7,5,4
twisted involution orbit size: 420; fiber size: 8; strong inv: 3360
imaginary root system: A1.A3.A1
real root system: A1.A1
complex factor: A1
real form #4: [0,2,4] (3)
real form #2: [1,3,5,7] (4)
real form #3: [6] (1)


Cartan #4:
split: 2; compact: 3; complex: 1
canonical twisted involution: 3,4,5,6,7,5,4,3,2,3,4,5,6,7,5,4,3,1,2,3,4,5,6,7,5,
    4,3,2,1
twisted involution orbit size: 420; fiber size: 8; strong inv: 3360
imaginary root system: A1.A3
real root system: A1.A1.A1
complex factor: A1
real form #4: [0,1,2] (3)
real form #3: [3] (1)


Cartan #6:
split: 4; compact: 3; complex: 0
canonical twisted involution: 3,4,5,6,7,5,4,3,2,3,4,5,6,7,5,4,3,2,1,2,3,4,5,6,7,
    5,4,3,2,1
twisted involution orbit size: 35; fiber size: 8; strong inv: 280
imaginary root system: A3
real root system: D4
complex factor: A1
real form #4: [0,1,2] (3)
real form #3: [3] (1)