Order = 5616 = 24.33.13.
Mult = 1.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of L3(3) are a, b where a has order 2, b is in class 3B and ab is in class 13A/B. Alternatively: a has order 2, b is in class 3B, ab has order 13 and ababb has order 4.
Standard generators of L3(3):2 are c, d where c is in class 2B, d is in class 4B and cd is in class 13AB. Alternatively: c is in class 2B, d is in class 4B, cd has order 13 and cdcdcdd has order 12.
Black box algorithms
Checking generators (semi-presentations)
| Group | Semi-presentation | File |
|---|---|---|
| L3(3) | 〈〈 a, b | some conditions 〉〉 | Download |
Representations
Representations of L3(3)
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 13 a Std Details 13 b Std Details 144 Std Details 234 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 12 Std Details 0 Z 13 Std Details 0 Z 26 a Std Details 0 Z[i2] 26 b Std Details 0 Z[i2] 26 c Std Details 0 Z 27 Std Details 0 Z 39 Std Details 0 Z 52 Std Details 0 Z 64 Std Details Char Ring Dimension ID Generators Description Link 2 GF(2) 12 Std Details 2 GF(16) 16 a Std Details 2 GF(2) 26 Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 3 a Std Details 3 GF(3) 3 b Std Details 3 GF(3) 6 a Std Details 3 GF(3) 6 b Std Details 3 GF(3) 7 Std Details 3 GF(3) 15 a Std Details 3 GF(3) 15 b Std Details 3 GF(3) 27 Std Details Char Ring Dimension ID Generators Description Link 13 GF(13) 11 Std Details 13 GF(13) 13 Std Details 13 GF(13) 16 Std Details 13 GF(13) 26 a Std Details 13 GF(169) 26 b Std Details 13 GF(169) 26 c Std Details 13 GF(13) 39 Std Details
Representations of L3(3):2
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 26 Std Details 52 Std Details 117 Std Details 144 Std Details 234 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 12 Std Details 2 GF(2) 26 Std Details 2 GF(4) 32 a Std Details 2 GF(4) 32 b Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 6 Std Details 3 GF(3) 7 a Std Details 3 GF(3) 12 Std Details 3 GF(3) 27 a Std Details 3 GF(3) 30 Std Details Char Ring Dimension ID Generators Description Link 13 GF(13) 11 a1 Std Details 13 GF(13) 13 a1 Std Details 13 GF(13) 16 a1 Std Details 13 GF(13) 26 a1 Std Details 13 GF(13) 39 a1 Std Details 13 GF(13) 52 Std Details