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: E8
real root system is empty
complex factor is empty
real form #2: [0,1,2,4,6,7,8,9,11,12,16,17,18,20,22,23,24,25,27,28,32,33,35,36,
40,41,42,44,46,47,50,53,54,55,59,61,64,65,66,68,70,71,72,73,75,76,80,81,82,
84,86,87,88,89,91,92,96,97,99,100,104,105,106,108,110,111,114,117,118,119,
123,125,128,129,131,132,136,137,138,140,142,143,146,149,150,151,155,157,160,
161,162,164,166,167,168,169,171,172,176,177,178,180,182,183,184,185,187,188,
194,197,198,199,203,205,208,209,211,212,216,217,218,220,222,223,227,229,234,
237,238,239,243,245,250,253,254] (135)
real form #1: [3,5,10,13,14,15,19,21,26,29,30,31,34,37,38,39,43,45,48,49,51,52,
56,57,58,60,62,63,67,69,74,77,78,79,83,85,90,93,94,95,98,101,102,103,107,
109,112,113,115,116,120,121,122,124,126,127,130,133,134,135,139,141,144,145,
147,148,152,153,154,156,158,159,163,165,170,173,174,175,179,181,186,189,190,
191,192,193,195,196,200,201,202,204,206,207,210,213,214,215,219,221,224,225,
226,228,230,231,232,233,235,236,240,241,242,244,246,247,248,249,251,
252] (120)
real form #0: [255] (1)
Cartan #1:
split: 0; compact: 6; complex: 1
canonical twisted involution: 8,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,
5,6,7,8,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7,8
twisted involution orbit size: 120; fiber size: 64; strong inv: 7680
imaginary root system: E7
real root system: A1
complex factor is empty
real form #2: [0,1,2,4,6,7,8,9,11,12,16,17,18,20,22,23,24,25,27,28,32,33,35,36,
40,41,42,44,46,47,50,53,54,55,59,61] (36)
real form #1: [3,5,10,13,14,15,19,21,26,29,30,31,34,37,38,39,43,45,48,49,51,52,
56,57,58,60,62,63] (28)
Cartan #2:
split: 0; compact: 4; complex: 2
canonical twisted involution: 1,3,4,2,5,4,3,1,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,
5,4,2,6,5,4,3,1,8,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,8,7,6,
5,4,2,3,1,4,3,5,4,2,6,5,4,3,1
twisted involution orbit size: 3780; fiber size: 16; strong inv: 60480
imaginary root system: D6
real root system: A1.A1
complex factor: A1
real form #2: [0,1,2,4,5,6,8,10,11,13] (10)
real form #1: [3,7,9,12,14,15] (6)
Cartan #3:
split: 0; compact: 2; complex: 3
canonical twisted involution: 7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,
6,7,8,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7,8,7,6,5,4,2,3,1,
4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7
twisted involution orbit size: 37800; fiber size: 4; strong inv: 151200
imaginary root system: D4.A1
real root system: A1.A1.A1
complex factor: A2
real form #2: [0,1,2] (3)
real form #1: [3] (1)
Cartan #4:
split: 0; compact: 0; complex: 4
canonical twisted involution: 2,4,3,1,5,4,2,3,4,5,6,5,4,2,3,1,4,3,5,4,2,7,6,5,4,
2,3,1,4,3,5,4,2,6,5,4,3,7,6,5,4,2,8,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,
4,2,3,4,5,6,7,8,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,7,6,5,4,2
twisted involution orbit size: 113400; fiber size: 1; strong inv: 113400
imaginary root system: A1.A1.A1.A1
real root system: A1.A1.A1.A1
complex factor: A3
real form #2: [0] (1)
Cartan #5:
split: 2; compact: 2; complex: 2
canonical twisted involution: 7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,
6,7,8,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7,8,7,6,5,4,2,3,1,
4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7,8
twisted involution orbit size: 3150; fiber size: 4; strong inv: 12600
imaginary root system: D4
real root system: D4
complex factor: A2
real form #2: [0,1,2] (3)
real form #1: [3] (1)
Cartan #6:
split: 2; compact: 0; complex: 3
canonical twisted involution: 2,4,3,1,5,4,2,3,4,5,6,5,4,2,3,1,4,3,5,4,2,7,6,5,4,
2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7,8,7,6,5,4,2,3,1,4,3,5,4,2,6,5,
4,3,1,7,6,5,4,2,3,4,5,6,7,8,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,
5,6,7,8
twisted involution orbit size: 37800; fiber size: 1; strong inv: 37800
imaginary root system: A1.A1.A1
real root system: D4.A1
complex factor: A2
real form #2: [0] (1)
Cartan #7:
split: 4; compact: 0; complex: 2
canonical twisted involution: 1,2,3,1,4,2,3,1,4,5,4,2,3,1,4,3,5,6,5,4,2,3,1,4,3,
5,4,2,6,5,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7,8,7,6,5,4,2,
3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7,8,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,
3,1,7,6,5,4,2,3,4,5,6,7,8
twisted involution orbit size: 3780; fiber size: 1; strong inv: 3780
imaginary root system: A1.A1
real root system: D6
complex factor: A1
real form #2: [0] (1)
Cartan #8:
split: 6; compact: 0; complex: 1
canonical twisted involution: 1,2,3,1,4,2,3,1,4,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,1,
4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7,8,
7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7,8,7,6,5,4,2,3,1,4,3,5,
4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7,8
twisted involution orbit size: 120; fiber size: 1; strong inv: 120
imaginary root system: A1
real root system: E7
complex factor is empty
real form #2: [0] (1)
Cartan #9:
split: 8; compact: 0; complex: 0
canonical twisted involution: 1,2,3,1,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,
1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7,
8,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7,8,7,6,5,4,2,3,1,4,3,
5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7,8
twisted involution orbit size: 1; fiber size: 1; strong inv: 1
imaginary root system is empty
real root system: E8
complex factor is empty
real form #2: [0] (1)