Order = 175560 = 23.3.5.7.11.19.
Mult = 1.
Out = 1.
Porting notes
Porting incomplete.Standard generators
Standard generators of J1 are a, b where a has order 2, b has order 3, ab has order 7 and ababb has order 19.
Black box algorithms
Finding generators
| Group | Algorithm | File |
|---|---|---|
| J1 |
| Download |
Checking generators (semi-presentations)
| Group | Semi-presentation | File |
|---|---|---|
| J1 | 〈〈 a, b | o(a) = 2, o(b) = 3, o(ab) = 7, o(abab2) = 19 〉〉 | Download |
Presentations
| Group | Presentation | Link |
|---|---|---|
| J1 | 〈 a, b | a2 = b3 = (ab)7 = (ab(abab−1)3)5 = (ab(abab−1)6abab(ab−1)2)2 = 1 〉 | Details |
Representations
Representations of J1
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 266 Std Details 1045 Std Details 1463 Std Details 1540 Std Details 1596 Std Details 2926 Std Details 4180 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 76 a Std Details 0 Z 76 b Std Details 0 Z 77 a Std Details 0 Z 112 Std Details 0 Z 133 a Std Details 0 Z 154 a Std Details 0 Z 209 Std Details 0 Z 266 Std Details 0 Z 360 Std Details Char Ring Dimension ID Generators Description Link 2 GF(2) 20 Std Details 2 GF(4) 56 a Std Details 2 GF(4) 56 b Std Details 2 GF(4) 56 c Std Details 2 GF(4) 56 d Std Details 2 GF(2) 76 a Std Details 2 GF(2) 76 b Std Details 2 GF(2) 112 a Std Details 2 GF(2) 112 b Std Details 2 GF(8) 120 a Std Details 2 GF(8) 120 b Std Details 2 GF(8) 120 c Std Details 2 GF(2) 360 Std Details Char Ring Dimension ID Generators Description Link 3 GF(9) 56 a Std Details 3 GF(9) 56 b Std Details 3 GF(3) 76 a Std Details 3 GF(3) 76 b Std Details 3 GF(9) 77 a Std Details 3 GF(9) 77 b Std Details 3 GF(3) 112 Std Details 3 GF(27) 120 a Std Details 3 GF(27) 120 b Std Details 3 GF(27) 120 c Std Details 3 GF(3) 133 Std Details 3 GF(3) 154 Std Details 3 GF(3) 360 Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 56 Std Details 5 GF(5) 76 a Std Details 5 GF(5) 76 b Std Details 5 GF(5) 77 Std Details 5 GF(125) 120 a Std Details 5 GF(125) 120 b Std Details 5 GF(125) 120 c Std Details 5 GF(5) 133 Std Details 5 GF(5) 360 Std Details Char Ring Dimension ID Generators Description Link 7 GF(7) 31 Std Details 7 GF(7) 45 Std Details 7 GF(49) 56 a Std Details 7 GF(49) 56 b Std Details 7 GF(7) 75 Std Details 7 GF(7) 77 a Std Details 7 GF(49) 77 b Std Details 7 GF(49) 77 c Std Details 7 GF(7) 89 Std Details 7 GF(7) 112 Std Details 7 GF(7) 120 Std Details 7 GF(7) 133 a Std Details 7 GF(49) 133 b Std Details 7 GF(49) 133 c Std Details 7 GF(7) 154 Std Details 7 GF(7) 266 Std Details Char Ring Dimension ID Generators Description Link 11 GF(11) 7 Std Details 11 GF(11) 14 Std Details 11 GF(11) 27 Std Details 11 GF(11) 49 Std Details 11 GF(11) 56 Std Details 11 GF(11) 64 Std Details 11 GF(11) 69 Std Details 11 GF(11) 77 a Std Details 11 GF(11) 77 b Std Details 11 GF(11) 77 c Std Details 11 GF(11) 106 Std Details 11 GF(11) 119 Std Details 11 GF(11) 209 Std Details Char Ring Dimension ID Generators Description Link 19 GF(19) 22 Std Details 19 GF(19) 34 Std Details 19 GF(19) 43 Std Details 19 GF(19) 55 Std Details 19 GF(19) 76 a Std Details 19 GF(19) 76 b Std Details 19 GF(19) 77 Std Details 19 GF(19) 133 a Std Details 19 GF(19) 133 b Std Details 19 GF(19) 133 c Std Details 19 GF(19) 209 Std Details
Maximal subgroups
Maximal subgroups of J1
| Subgroup | Order | Index | Programs/reps |
|---|---|---|---|
| L2(11) | Program: Standard generators | ||
| 23:7:3 = F168 | Program: Generators | ||
| 2 × A5 | Program: Generators | ||
| 19:6 = F114 | Program: Generators | ||
| 11:10 = F110 | Program: Generators | ||
| D6 × D10 | Program: Generators | ||
| 7:6 = F42 | Program: Generators |
Conjugacy classes
Conjugacy classes of J1
| Conjugacy class | Centraliser order | Power up | Class rep(s) |
|---|---|---|---|
| 1A | 175 560 |
(ababbababbabababbabbababbababbabababbabb)3 | |
| 2A | 120 | 6A 10A 10B |
(ababbababbabababbabb)3 |
| 3A | 30 | 6A 15A 15B |
ababbababbabababbabbababbababbabababbabb |
| 5A | 30 | 5B2 10A 10B 15A 15B |
ababbabababbabbababbabababbabb ababbabababbabbababbabababbabb |
| 5B | 30 | 5A2 10A 10B 15A 15B |
ababbabababbabbababbabababbabbababbabababbabbababbabababbabb |
| 6A | 6 |
ababbababbabababbabb ababbababbabababbabb | |
| 7A | 7 |
ab ab | |
| 10A | 10 | 10B3 |
(ababbabababbabb)3 |
| 10B | 10 | 10A3 |
ababbabababbabb ababbabababbabb ababbabababbabb |
| 11A | 11 |
abababbabbababbabababbabbababbabababbabb abababbabbababbabababbabbababbabababbabb | |
| 15A | 15 | 15B2 |
abababbabbabababbabb |
| 15B | 15 | 15A2 |
abababbabb abababbabb abababbabb |
| 19A | 19 | 19B4 19C2 |
ababb ababb ababb |
| 19B | 19 | 19A2 19C4 |
ababbababb |
| 19C | 19 | 19A4 19B2 |
ababbababbababbababb |
Download words for class representatives.