Order = 197406720 = 212.34.5.7.17.
Mult = 1.
Out = 2.

Porting notes

Fully copied from version 2. 29/7/06.

Standard generators

Standard generators of O8−(2) are a, b where a is in class 2C, b is in class 3C, ab has order 17, ababb has order 17 and abababb has order 30.

Standard generators of O8−(2):2 are c, d where c is in class 2D, d has order 14, cd has order 17 and cdcdd has order 12.

Representations

Representations of O8−(2)

Representations of O8−(2):2

Maximal subgroups

Maximal subgroups of O8−(2)

Subgroup Order Index Programs/reps
26:U4(2)
S6(2)
2(3+6):(L3(2) × 3)
2(1+8):(S3 × A5)
(3 x A8):2
L2(16):2
(S3 × S3 × A5):2
L2(7)

Maximal subgroups of O8−(2):2

Subgroup Order Index Programs/reps
O8-(2)
26:U4(2):2
S6(2) × 2
2(3+6):(L3(2) × S3)
2(1+8):(S3 × S5)
S3 × S8
L2(16):4
(S3 × S3):2 × S5
L2(7):2

Conjugacy classes

Conjugacy classes of O8−(2)

Conjugacy class Centraliser order Power up Class rep(s)
1A 197 406 720 Omitted owing to length.
2A 184 320 ababababbabababababbabababababbabababababbab
2B 46 080 (ababbaababababbababababbababb)3
2C 3 072 Omitted owing to length.
3A 60 480 Omitted owing to length.
3B 1 080 abababbababababbababababbababbabababbababababbababababbababb
3C 648 Omitted owing to length.
4A 1 536 abababbababababbab
4B 1 536 ababababbabababababbab
4C 192 (ababababbababababbabababbababbaababababbababababbababb)3
4D 64 ababababbababababbababbababbaababababbababababbababb
5A 180 ababababbababababbabababababbababababbab
6A 576 ababababbababababbababbababababbababababbababb
6B 360 (abababb)5
6C 288 Omitted owing to length.
6D 72 Omitted owing to length.
6E 72 ababbaababababbababababbababb
6F 24 abababbababababbababababbababb
7A 21 (abababbabb)3
8A 32 abababbab
8B 32 ababababbab
9A 9 aababababbababababbababb
10A 60 (abababb)9
10B 60 (abababb)3
10C 20 ababababbababababbab
12A 48 ababababbababababbababb
12B 24 ababababbababababbabababbababbaababababbababababbababb
12C 12 ababbababbababbaababababbababababbababb
15A 90 abababbabababbabababbabababb
15B 90 abababbabababb
15C 45 ababbababbaababababbababababbababb
17A 17 ab
17B 17 abab
17C 17 (ab)3
17D 17 (abab)3
21A 21 abababbabb
21B 21 abababbabbabababbabb
30A 30 abababb
30B 30 (abababb)7

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Conjugacy classes of O8−(2):2

Conjugacy class Centraliser order Power up Class rep(s)
1A 394 813 440 (cdcdcddcdcddcddcdcddcdd)4
2A 368 640 (cdcddcdcddcddd)4
2B 92 160 (cdcdcddcdcddcddcdcddcdd)2
2C 6 144 (cdcdcdcdd)4
3A 120 960 (cdcdcddcdcdcdcddcdcdcdcdd)2
3B 2 160 (cdcdcdcddcdcddcddd)2
3C 1 296 (cdcddcdcdcdcddcdcddcdddcdcdcdcddcdcddcddd)2
4A 3 072 (cdcddcdcddcddd)2
4B 3 072 (cdcdcddcdcddcddcdcddcddcdcdcdd)2
4C 384 (cdcdcddcdcddcddcdcdcddcdcddcddcdcddcdd)3
4D 128 (cdcdcdcdd)2
5A 360 (cdcdcdcddcdcdcddd)4
6A 1 152 (cdcddcddd)4
6B 720 (cdcdcddcdcddcddcdcdcdddcdd)5
6C 576 (cdcdcddcdcddcddcdcdcddcdcddcddcdcddcdd)2
6D 144 (cdcddcdd)2
6E 144 (cdcddcdcddcdcddcddd)2
6F 48 cdcdcdcddcdcddcddd
7A 42 (d)2
8A 64 cdcddcdcddcddd
8B 64 cdcdcddcdcddcddcdcddcddcdcdcdd
9A 18 (cdd)2
10A 60 (cdcdcddcdcddcddcdcdcdddcdd)3
10C 40 (cdcdcdcddcdcdcddd)2
12A 96 (cdcddcddd)2
12B 48 cdcdcddcdcddcddcdcdcddcdcddcddcdcddcdd
12C 24 cdcddcdd
15A 90 (cdcdcddcdcddcddcdcdcdddcdd)2
15C 90 (cdcdcddcdcddcdd)2
17A 17 cd
17C 17 (cd)3
21A 21 cdcdcddd
30A 30 cdcdcddcdcddcddcdcdcdddcdd
2D 2 903 040 (cdcdcdddcdcddcddd)3
2E 9 216 (cdcdcdcddcdcddcdddcdcdcdddcdcddcddd)3
4E 7 680 (cdcdcdddcdd)3
4F 4 608 (cdcddcdcddcdcddcddd)3
4G 768 (cdcdd)3
4H 768 (cdcdcdd)3
4I 256 cdcdcddcdcddcddcdcddcdd
6G 4 320 (cdcdcddcdcddcdd)5
6H 1 296 (cdd)3
6I 288 cdcdcddcdcdcdcddcdcdcdcdd
6J 216 cdcdcdddcdcddcddd
6K 144 cdcddcdcdcdcddcdcddcdddcdcdcdcddcdcddcddd
6L 72 cdcdcdcddcdcddcdddcdcdcdddcdcddcddd
8C 192 (cdcddcddd)3
8D 64 cdcddcdcddcdddcdcdcdd
8E 16 cdcdcdcdd
10D 60 (cdcdcddcdcddcdd)3
12D 288 cdcdcddcdcddcddcdcdcddcdcddcddcdcddcddcdcdcdddcdd
12E 96 cdcdcdddcdd
12F 72 cdcddcdcddcdcddcddd
12G 24 cdcdd
12H 24 cdcdcdd
14A 14 d
18A 18 cdd
20A 20 cdcdcdcddcdcdcddd
24A 24 cdcddcddd
30C 30 cdcdcddcdcddcdd

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