Order = 145926144000 = 214.33.53.7.13.29.
Mult = 2.
Out = 1.
Porting notes
Porting incomplete.Standard generators
Standard generators of Ru are a, b where a is in class 2B, b is in class 4A and ab has order 13.
Standard generators of 2.Ru are preimages A, B where B is in class +4A and AB has order 13. Alternatively: AB has order 13 and ABABB has order 29.
Black box algorithms
Finding generators
| Group | Algorithm | File |
|---|---|---|
| Ru |
| Download |
Checking generators (semi-presentations)
| Group | Semi-presentation | File |
|---|---|---|
| Ru | 〈〈 a, b | o(a) = 2, o(b) = 4, o(ab) = 13, o(abb) = 14, o(ababb) = 29 〉〉 | Download |
Representations
Representations of Ru
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 4060 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 28 Std Details 2 GF(2) 376 Std Details 2 GF(2) 1246 Std Details Char Ring Dimension ID Generators Description Link 3 GF(9) 378 Std Details 3 GF(3) 406 Std Details 3 GF(3) 783 Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 133 Std Details 5 GF(5) 273 Std Details 5 GF(5) 378 Std Details 5 GF(5) 783 Std Details Char Ring Dimension ID Generators Description Link 7 GF(49) 378 Std Details 7 GF(7) 406 Std Details 7 GF(7) 782 Std Details Char Ring Dimension ID Generators Description Link 13 GF(13) 378 Std Details 13 GF(13) 406 Std Details 13 GF(13) 783 Std Details Char Ring Dimension ID Generators Description Link 29 GF(29) 378 Std Details 29 GF(29) 406 Std Details 29 GF(29) 783 Std Details
Representations of 2.Ru
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 16240 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(9) 28 Std Details 3 GF(3) 56 Std Details 5 GF(5) 28 Std Details 5 GF(5) 912 Std Details 7 GF(49) 28 Std Details 7 GF(7) 56 Std Details 13 GF(13) 28 Std Details 29 GF(29) 28 Std Details
Maximal subgroups
Maximal subgroups of Ru
| Subgroup | Order | Index | Programs/reps |
|---|---|---|---|
| 2F4(2) = 2F4(2)'.2 | Program: Generators Program: Generators | ||
| 26.U3(3).2 | Program: Generators Program: Generators | ||
| (22 × Sz(8)):3 | Program: Generators Program: Generators | ||
| 23+8:L3(2) | Program: Generators Program: Generators | ||
| U3(5):2 | Program: Generators Program: Generators | ||
| 21+4+6.S5 | Program: Generators Program: Generators | ||
| L2(25).22 | Program: Generators Program: Generators | ||
| A8 | Program: Generators Program: Generators | ||
| L2(29) | Program: Generators Program: Generators Program: Generators | ||
| 52:4.S5 | Program: Generators Program: Generators | ||
| 3.A6.22 | Program: Generators Program: Generators | ||
| 51+2:[25] | Program: Generators Program: Generators | ||
| L2(13):2 | Program: Generators Program: Generators | ||
| A6.22 | Program: Generators Program: Generators | ||
| 5:4 × A5 | Program: Generators Program: Generators Program: Generators |
Conjugacy classes
Conjugacy classes of Ru
| Conjugacy class | Centraliser order | Power up | Class rep(s) |
|---|---|---|---|
| 1A | 145 926 144 000 | ||
| 2A | 245 760 | 4A 4B 4C 4D 6A 8A 8B 8C 10A 12A 12B 16A 16B 20A 20B 20C 24A 24B | |
| 2B | 116 480 | 10B 14A 14B 14C 26A 26B 26C | |
| 3A | 2 160 | 6A 12A 12B 15A 24A 24B | |
| 4A | 7 680 | 8A 12A 20A 24A 24B | |
| 4B | 3 840 | 12B 20B 20C | |
| 4C | 1 024 | 8B 16A 16B | |
| 4D | 512 | 8C | |
| 5A | 1 000 | 10A 20A 20B 20C | |
| 5B | 300 | 10B 15A | |
| 6A | 48 | 12A 12B 24A 24B | |
| 7A | 28 | 14A 14B 14C | |
| 8A | 96 | 24A 24B | |
| 8B | 64 | 16A 16B | |
| 8C | 32 |
babbabababbababbabbababbabbabbabbabababbababbabb | |
| 10A | 40 | 20A 20B 20C | |
| 10B | 20 |
abbabababbababbabbababbabbbbabbabababbababbabbababbabbabb | |
| 12A | 24 | 24A 24B | |
| 12B | 12 |
abababbababbabb | |
| 13A | 52 | 26A 26B 26C | |
| 14A | 28 | 14B5 14C3 | |
| 14B | 28 | 14A3 14C5 | |
| 14C | 28 | 14A5 14B3 | |
| 15A | 15 |
ababbababbabb | |
| 16A | 16 | 16B3 |
babbabababbababbabbababbabb |
| 16B | 16 | 16A3 | |
| 20A | 20 |
abababbabb | |
| 20B | 20 | 20C3 | |
| 20C | 20 | 20B3 | |
| 24A | 24 | 24B7 | |
| 24B | 24 | 24A7 |
abbabababbababbabb |
| 26A | 52 | 26B7 26C3 | |
| 26B | 52 | 26A3 26C7 |
bababbabb |
| 26C | 52 | 26A7 26B3 | |
| 29A | 29 | 29B2 |
ababb |
| 29B | 29 | 29A2 | |
| 14A-C |
abb | ||
| 20B-C |
abbabababbababbabbababbabb |
Download words for class representatives.