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)
1A197 406 720 Omitted owing to length.
2A184 320 ababababbabababababbabababababbabababababbab
2B46 080 (ababbaababababbababababbababb)3
2C3 072 Omitted owing to length.
3A60 480 Omitted owing to length.
3B1 080 abababbababababbababababbababbabababbababababbababababbababb
3C648 Omitted owing to length.
4A1 536 abababbababababbab
4B1 536 ababababbabababababbab
4C192 (ababababbababababbabababbababbaababababbababababbababb)3
4D64 ababababbababababbababbababbaababababbababababbababb
5A180 ababababbababababbabababababbababababbab
6A576 ababababbababababbababbababababbababababbababb
6B360 (abababb)5
6C288 Omitted owing to length.
6D72 Omitted owing to length.
6E72 ababbaababababbababababbababb
6F24 abababbababababbababababbababb
7A21 (abababbabb)3
8A32 abababbab
8B32 ababababbab
9A9 aababababbababababbababb
10A60 (abababb)9
10B60 (abababb)3
10C20 ababababbababababbab
12A48 ababababbababababbababb
12B24 ababababbababababbabababbababbaababababbababababbababb
12C12 ababbababbababbaababababbababababbababb
15A90 abababbabababbabababbabababb
15B90 abababbabababb
15C45 ababbababbaababababbababababbababb
17A17 ab
17B17 abab
17C17 (ab)3
17D17 (abab)3
21A21 abababbabb
21B21 abababbabbabababbabb
30A30 abababb
30B30 (abababb)7

Download words for class representatives.

Conjugacy classes of O8(2):2

Conjugacy class Centraliser order Power up Class rep(s)
1A394 813 440 (cdcdcddcdcddcddcdcddcdd)4
2A368 640 (cdcddcdcddcddd)4
2B92 160 (cdcdcddcdcddcddcdcddcdd)2
2C6 144 (cdcdcdcdd)4
3A120 960 (cdcdcddcdcdcdcddcdcdcdcdd)2
3B2 160 (cdcdcdcddcdcddcddd)2
3C1 296 (cdcddcdcdcdcddcdcddcdddcdcdcdcddcdcddcddd)2
4A3 072 (cdcddcdcddcddd)2
4B3 072 (cdcdcddcdcddcddcdcddcddcdcdcdd)2
4C384 (cdcdcddcdcddcddcdcdcddcdcddcddcdcddcdd)3
4D128 (cdcdcdcdd)2
5A360 (cdcdcdcddcdcdcddd)4
6A1 152 (cdcddcddd)4
6B720 (cdcdcddcdcddcddcdcdcdddcdd)5
6C576 (cdcdcddcdcddcddcdcdcddcdcddcddcdcddcdd)2
6D144 (cdcddcdd)2
6E144 (cdcddcdcddcdcddcddd)2
6F48 cdcdcdcddcdcddcddd
7A42 (d)2
8A64 cdcddcdcddcddd
8B64 cdcdcddcdcddcddcdcddcddcdcdcdd
9A18 (cdd)2
10A60 (cdcdcddcdcddcddcdcdcdddcdd)3
10C40 (cdcdcdcddcdcdcddd)2
12A96 (cdcddcddd)2
12B48 cdcdcddcdcddcddcdcdcddcdcddcddcdcddcdd
12C24 cdcddcdd
15A90 (cdcdcddcdcddcddcdcdcdddcdd)2
15C90 (cdcdcddcdcddcdd)2
17A17 cd
17C17 (cd)3
21A21 cdcdcddd
30A30 cdcdcddcdcddcddcdcdcdddcdd
2D2 903 040 (cdcdcdddcdcddcddd)3
2E9 216 (cdcdcdcddcdcddcdddcdcdcdddcdcddcddd)3
4E7 680 (cdcdcdddcdd)3
4F4 608 (cdcddcdcddcdcddcddd)3
4G768 (cdcdd)3
4H768 (cdcdcdd)3
4I256 cdcdcddcdcddcddcdcddcdd
6G4 320 (cdcdcddcdcddcdd)5
6H1 296 (cdd)3
6I288 cdcdcddcdcdcdcddcdcdcdcdd
6J216 cdcdcdddcdcddcddd
6K144 cdcddcdcdcdcddcdcddcdddcdcdcdcddcdcddcddd
6L72 cdcdcdcddcdcddcdddcdcdcdddcdcddcddd
8C192 (cdcddcddd)3
8D64 cdcddcdcddcdddcdcdcdd
8E16 cdcdcdcdd
10D60 (cdcdcddcdcddcdd)3
12D288 cdcdcddcdcddcddcdcdcddcdcddcddcdcddcddcdcdcdddcdd
12E96 cdcdcdddcdd
12F72 cdcddcdcddcdcddcddd
12G24 cdcdd
12H24 cdcdcdd
14A14 d
18A18 cdd
20A20 cdcdcdcddcdcdcddd
24A24 cdcddcddd
30C30 cdcdcddcdcddcdd

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