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)
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 119 Std Details 136 Std Details 765 Std Details 1071 Std Details 1632 Std Details 24192 Std Details 45696 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 34 Std Details 0 Z 51 Std Details 0 Z 84 Std Details 0 Z 204 a Std Details 0 Z 204 b Std Details Char Ring Dimension ID Generators Description Link 2 GF(2) 8 Std Details 2 GF(4) 8 b Std Details 2 GF(4) 8 c Std Details 2 GF(2) 26 Std Details 2 GF(2) 48 Std Details 2 GF(4) 48 b Std Details 2 GF(4) 48 c Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 34 Std Details 3 GF(3) 50 Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 34 Std Details 5 GF(5) 51 Std Details 5 GF(5) 84 Std Details Char Ring Dimension ID Generators Description Link 7 GF(7) 33 Std Details 7 GF(7) 51 Std Details 7 GF(7) 84 Std Details Char Ring Dimension ID Generators Description Link 17 GF(17) 34 Std Details 17 GF(17) 51 Std Details 17 GF(17) 83 Std Details
Representations of O8−(2):2
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 119 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 8 Std Details 3 GF(3) 34 Std Details 3 GF(3) 50 Std Details
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 |
Download words for class representatives.
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 |
Download words for class representatives.