
Cartan #0:
split: 0; compact: 8; complex: 0
canonical twisted involution: e
twisted involution orbit size: 1; fiber size: 256; strong inv: 256
imaginary root system: D8
real root system is empty
complex factor is empty
real form #6: [0,2,5,8,10,13,17,20,22,27,32,34,37,40,42,45,49,52,54,59,193,196,
    198,203,208,210,213,216,218,221,227,233,236,238,247] (35)
real form #5: [1,3,4,6,9,11,12,14,16,18,21,23,24,26,29,33,35,36,38,41,43,44,46,
    48,50,53,55,56,58,61,192,194,197,199,200,202,205,209,211,212,214,217,219,
    220,222,224,226,229,232,234,237,239,241,244,246,251] (56)
real form #2: [7,15,19,25,28,30,39,47,51,57,60,62,195,201,204,206,215,223,225,
    228,230,235,240,242,245,248,250,253] (28)
real form #1: [31,63,207,231,243,249,252,254] (8)
real form #3: [64,66,69,71,72,74,77,79,81,83,84,86,89,91,92,94,96,98,101,103,
    104,106,109,111,113,115,116,118,121,123,124,126,129,131,132,134,137,139,140,
    142,144,146,149,151,152,154,157,159,161,163,164,166,169,171,172,174,176,178,
    181,183,184,186,189,191] (64)
real form #4: [65,67,68,70,73,75,76,78,80,82,85,87,88,90,93,95,97,99,100,102,
    105,107,108,110,112,114,117,119,120,122,125,127,128,130,133,135,136,138,141,
    143,145,147,148,150,153,155,156,158,160,162,165,167,168,170,173,175,177,179,
    180,182,185,187,188,190] (64)
real form #0: [255] (1)


Cartan #1:
split: 0; compact: 6; complex: 1
canonical twisted involution: 2,3,4,5,6,7,8,6,5,4,3,2,1,2,3,4,5,6,7,8,6,5,4,3,2
twisted involution orbit size: 56; fiber size: 64; strong inv: 3584
imaginary root system: A1.D6
real root system: A1
complex factor is empty
real form #6: [0,4,10,16,20,26,34,40,44,54] (10)
real form #3: [1,5,11,15,17,21,27,31,35,39,41,45,51,55,57,61] (16)
real form #5: [2,6,8,12,18,22,24,28,32,36,42,46,48,52,58] (15)
real form #4: [3,7,9,13,19,23,25,29,33,37,43,47,49,53,59,63] (16)
real form #2: [14,30,38,50,56,60] (6)
real form #1: [62] (1)


Cartan #2:
split: 2; compact: 6; complex: 0
canonical twisted involution: 1,2,3,4,5,6,7,8,6,5,4,3,2,1
twisted involution orbit size: 28; fiber size: 64; strong inv: 1792
imaginary root system: D6
real root system: A1.A1
complex factor: A1
real form #6: [0,2,5,8,10,13,17,20,22,27] (10)
real form #5: [1,3,4,6,9,11,12,14,16,18,21,23,24,26,29] (15)
real form #2: [7,15,19,25,28,30] (6)
real form #1: [31] (1)


Cartan #3:
split: 0; compact: 4; complex: 2
canonical twisted involution: 4,5,6,7,8,6,5,4,3,4,5,6,7,8,6,5,4,2,3,4,5,6,7,8,6,
    5,4,1,2,3,4,5,6,7,8,6,5,4
twisted involution orbit size: 840; fiber size: 16; strong inv: 13440
imaginary root system: A1.D4.A1
real root system: A1.A1
complex factor: A1
real form #6: [0,4,10] (3)
real form #4: [1,5,11,15] (4)
real form #5: [2,6,8,12] (4)
real form #3: [3,7,9,13] (4)
real form #2: [14] (1)


Cartan #4:
split: 2; compact: 4; complex: 1
canonical twisted involution: 3,4,5,6,7,8,6,5,4,3,2,3,4,5,6,7,8,6,5,4,3,1,2,3,4,
    5,6,7,8,6,5,4,3,2,1
twisted involution orbit size: 840; fiber size: 16; strong inv: 13440
imaginary root system: A1.D4
real root system: A1.A1.A1
complex factor: A1
real form #6: [0,2,5] (3)
real form #5: [1,3,4,6] (4)
real form #2: [7] (1)


Cartan #5:
split: 0; compact: 2; complex: 3
canonical twisted involution: 6,7,8,6,5,6,7,8,6,4,5,6,7,8,6,3,4,5,6,7,8,6,2,3,4,
    5,6,7,8,6,1,2,3,4,5,6,7,8,6
twisted involution orbit size: 3360; fiber size: 4; strong inv: 13440
imaginary root system: A1.A1.A1.A1.A1
real root system: A1.A1.A1
complex factor: A2
real form #6: [0] (1)
real form #3: [1] (1)
real form #5: [2] (1)
real form #4: [3] (1)


Cartan #6:
split: 4; compact: 4; complex: 0
canonical twisted involution: 3,4,5,6,7,8,6,5,4,3,2,3,4,5,6,7,8,6,5,4,3,2,1,2,3,
    4,5,6,7,8,6,5,4,3,2,1
twisted involution orbit size: 70; fiber size: 16; strong inv: 1120
imaginary root system: D4
real root system: D4
complex factor: A1
real form #6: [0,2,5] (3)
real form #5: [1,3,4,6] (4)
real form #2: [7] (1)


Cartan #7:
split: 2; compact: 2; complex: 2
canonical twisted involution: 5,6,7,8,6,5,4,5,6,7,8,6,5,3,4,5,6,7,8,6,5,2,3,4,5,
    6,7,8,6,5,1,2,3,4,5,6,7,8,6,5,4,3,2,1
twisted involution orbit size: 5040; fiber size: 4; strong inv: 20160
imaginary root system: A1.A1.A1.A1
real root system: A1.A1.A1.A1
complex factor: A1.A1
real form #6: [0] (1)
real form #5: [1] (1)


Cartan #10:
split: 4; compact: 2; complex: 1
canonical twisted involution: 5,6,7,8,6,5,4,5,6,7,8,6,5,3,4,5,6,7,8,6,5,4,3,2,3,
    4,5,6,7,8,6,5,4,3,2,1,2,3,4,5,6,7,8,6,5,4,3,2,1
twisted involution orbit size: 840; fiber size: 4; strong inv: 3360
imaginary root system: A1.A1.A1
real root system: D4.A1
complex factor: A1
real form #6: [0] (1)
real form #5: [1] (1)


Cartan #12:
split: 6; compact: 2; complex: 0
canonical twisted involution: 5,6,7,8,6,5,4,5,6,7,8,6,5,4,3,4,5,6,7,8,6,5,4,3,2,
    3,4,5,6,7,8,6,5,4,3,2,1,2,3,4,5,6,7,8,6,5,4,3,2,1
twisted involution orbit size: 28; fiber size: 4; strong inv: 112
imaginary root system: A1.A1
real root system: D6
complex factor: A1
real form #6: [0] (1)
real form #5: [1] (1)

