Order = 20160 = 26.32.5.7.
Mult = 3 × 4 × 4.
Out = 2 × S3 = D12.
This group has too much information to appear conveniently on one page. We have decided to split it into subpages.
- L3(4) and its covers
- L3(4):2a and its 'covers'
- L3(4):2b and its 'covers'
- L3(4):2c and its 'covers'
- L3(4):3 and its 'covers'
- L3(4):6 and its 'covers'
- L3(4):22 and its 'covers'
- L3(4):3:2b and its 'covers'
- L3(4):3:2c and its 'covers'
- L3(4):D12 and its 'covers'
Porting notes
Porting incomplete.Standard generators
Standard generators of L3(4):2a are c, d where c is in class 2B, d is in class 4D and cd has order 7.
Standard generators of 3.L3(4):2a are preimages C, D where C has order 2 and D has order 4.
Standard generators of 4a.L3(4):2a are preimages C, D where CD has order 7 and CDD has order 8.
Standard generators of 2.L3(4):2a are preimages C, D where CD has order 7 and CDCDCDDCDCDD has order 3.
Standard generators of 4b.L3(4):2a are preimages C, D where CD has order 7 and CDD has order 8.
Standard generators of 6.L3(4):2a are preimages C, D where C has order 2, D has order 4, CD has order 21 and CDCDCDDCDCDD has order 3.
Standard generators of 12a.L3(4):2a are preimages C, D where C has order 2, D has order 4, CD has order 21 and CDD has order 8.
Standard generators of 12b.L3(4):2a are preimages C, D where C has order 2, D has order 4, CD has order 21 and CDD has order 8.
Representations
Representations of L3(4):2a
- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 16 a Std Details 2 GF(2) 18 a Std Details 2 GF(2) 64 a Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 15 a Std Details 3 GF(3) 15 b Std Details 3 GF(3) 15 c Std Details 3 GF(3) 19 a Std Details 3 GF(3) 90 a Std Details 3 GF(3) 126 a Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 20 a Std Details 5 GF(5) 35 a Std Details 5 GF(5) 35 b Std Details 5 GF(5) 35 c Std Details 5 GF(5) 63 a Std Details 5 GF(5) 90 a Std Details Char Ring Dimension ID Generators Description Link 7 GF(7) 19 a Std Details 7 GF(7) 35 a Std Details 7 GF(7) 35 b Std Details 7 GF(7) 35 c Std Details 7 GF(7) 45 a Std Details 7 GF(7) 126 a Std Details
Representations of 3.L3(4):2a
- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(4) 6 a Std Details 2 GF(4) 9 a Std Details 2 GF(4) 48 a Std Details Char Ring Dimension ID Generators Description Link 5 GF(25) 15 a Std Details 5 GF(25) 15 b Std Details 5 GF(25) 15 c Std Details 5 GF(25) 21 a Std Details 5 GF(25) 63 a Std Details 5 GF(25) 90 a Std Details Char Ring Dimension ID Generators Description Link 7 GF(7) 15 a Std Details 7 GF(7) 15 b Std Details 7 GF(7) 15 c Std Details 7 GF(7) 21 a Std Details 7 GF(7) 126 a Std Details
Representations of 4a.L3(4):2a
- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 16 a Std Details 3 GF(3) 16 b Std Details 3 GF(3) 48 a Std Details 3 GF(3) 48 b Std Details 3 GF(3) 80 a Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 16 a Std Details 5 GF(5) 112 a Std Details 5 GF(25) 160 a Std Details Char Ring Dimension ID Generators Description Link 7 GF(7) 16 a Std Details 7 GF(7) 16 b Std Details 7 GF(7) 112 a Std Details 7 GF(7) 128 a Std Details
Representations of 2.L3(4):2a
- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(9) 6 a Std Details 3 GF(3) 20 a Std Details 3 GF(3) 36 a Std Details 3 GF(3) 44 a Std Details 3 GF(9) 90 a Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 20 a Std Details 5 GF(5) 28 a Std Details 5 GF(5) 36 a Std Details 5 GF(25) 70 a Std Details 5 GF(25) 90 a Std Details Char Ring Dimension ID Generators Description Link 7 GF(7) 10 a Std Details 7 GF(7) 26 a Std Details 7 GF(7) 56 a Std Details 7 GF(7) 64 a Std Details 7 GF(7) 70 a Std Details
Representations of 4b.L3(4):2a
- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 8 a Std Details 3 GF(3) 32 a Std Details 3 GF(3) 56 a Std Details 3 GF(3) 56 b Std Details 3 GF(3) 72 a Std Details 3 GF(3) 120 a Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 40 a Std Details 5 GF(5) 56 a Std Details 5 GF(5) 72 a Std Details 5 GF(25) 160 a Std Details Char Ring Dimension ID Generators Description Link 7 GF(7) 40 a Std Details 7 GF(7) 56 a Std Details 7 GF(7) 56 b Std Details 7 GF(7) 72 a Std Details 7 GF(7) 88 a Std Details
Representations of 6.L3(4):2a
- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 5 GF(25) 6 a Std Details 5 GF(25) 36 a Std Details 5 GF(25) 90 a Std Details 5 GF(25) 120 a Std Details 7 GF(7) 6 a Std Details 7 GF(7) 36 a Std Details 7 GF(7) 54 a Std Details 7 GF(7) 84 a Std Details
Representations of 12a.L3(4):2a
- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 5 GF(25) 48 a Std Details 5 GF(25) 48 b Std Details 5 GF(25) 240 a Std Details 7 GF(7) 48 a Std Details 7 GF(7) 96 a Std Details 7 GF(7) 96 b Std Details
Representations of 12b.L3(4):2a
- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 5 GF(25) 72 a Std Details 5 GF(25) 96 a Std Details 5 GF(25) 120 a Std Details 5 GF(25) 120 b Std Details 7 GF(7) 24 a Std Details 7 GF(7) 72 a Std Details 7 GF(7) 96 a Std Details 7 GF(7) 168 a Std Details
Conjugacy classes
Conjugacy classes of L3(4):2a
| Conjugacy class | Centraliser order | Power up | Class rep(s) |
|---|---|---|---|
| 1A | 40 320 | ||
| 2A | 128 | ||
| 3A | 18 | ||
| 4A | 32 | ||
| 4B | 32 | ||
| 4C | 32 | ||
| 5A | 5 |
cdcddcdd |
|
| 7A | 7 | cd |
|
| 2B | 144 | ||
| 4D | 16 | d |
|
| 6A | 18 |
cdcddcddcdcddcddcdd |
|
| 8A | 8 | cdd |
|
| 8B | 8 |
cdcdcddcddd |
|
| 8C | 8 |
cdcddcddcdcddcddd |
Download words for class representatives.