Order = 20158709760 =
215.34.5.72.31.
Mult = 1.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of L6(2) are a, b where a is in class 2A, b is in class 6F, ab has order 63 and abb has order 6.
Standard generators of L6(2):2 are c, d where c is in class 2D, d is in class 7CD (i.e. the class of 7-elements with fixed points in the natural representation), cd has order 30 and cdd has order 14.
Black box algorithms
Checking generators (semi-presentations)
| Group | Semi-presentation | File |
|---|---|---|
| L6(2) | 〈〈 a, b | some conditions 〉〉 | Download |
Representations
Representations of L6(2)
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 63 a Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 62 Std Details 0 Z 217 Std Details Char Ring Dimension ID Generators Description Link 2 GF(2) 6 a Std Details 2 GF(2) 6 b Std Details 2 GF(2) 15 a Std Details 2 GF(2) 15 b Std Details 2 GF(2) 20 Std Details 2 GF(2) 34 Std Details 2 GF(2) 70 a Std Details 2 GF(2) 84 a Std Details 2 GF(2) 90 a Std Details 2 GF(2) 154 Std Details 2 GF(2) 204 a Std Details 2 GF(2) 384 a Std Details 2 GF(2) 400 Std Details 2 GF(2) 720 a Std Details 2 GF(2) 896 a Std Details 2 GF(2) 924 a Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 61 Std Details 3 GF(3) 527 a Std Details 3 GF(3) 651 a Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 62 Std Details Char Ring Dimension ID Generators Description Link 7 GF(7) 61 Std Details Char Ring Dimension ID Generators Description Link 31 GF(31) 62 Std Details
Representations of L6(2):2
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 126 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(2) 12 Std Details 2 GF(2) 20 Std Details 2 GF(2) 30 Std Details 2 GF(2) 34 Std Details 2 GF(2) 140 Std Details 2 GF(2) 154 Std Details 2 GF(2) 168 Std Details 2 GF(2) 180 Std Details 2 GF(2) 400 Std Details 2 GF(2) 408 Std Details 2 GF(2) 768 Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 61 Std Details Char Ring Dimension ID Generators Description Link 7 GF(7) 61 Std Details