Order = 24815256521932800 =
225.36.52.7.11.17.31.
Mult = 1.
Out = 1.
Porting notes
Porting incomplete.Standard generators
Standard generators of S10(2) are a, b where a is in class 2A (the class of transvections in the natural 10-dimensional representation), b has order 11 and ab has order 15.
Presentations
| Group | Presentation | Link |
|---|---|---|
| S10(2) | 〈 a, b | a2 = b11 = (ab)15 = (ab5)18 = [a, b]3 = [a, b2]2 = [a, b3]2 = [a, b4]2 = [a, b5]3 = [a, (ab)5]2 = 1 〉 | Details |
Representations
Representations of S10(2)
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 496 Std Details 528 Std Details 992 Std Details 1023 Std Details 1056 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 155 Std Details 0 Z 187 Std Details 0 Z 341 Std Details Char Ring Dimension ID Generators Description Link 2 GF(2) 10 Std Details 2 GF(2) 32 Std Details 2 GF(2) 44 Std Details 2 GF(2) 100 Std Details 2 GF(2) 164 Std Details Char Ring Dimension ID Generators Description Link 3 GF(3) 155 Std Details Char Ring Dimension ID Generators Description Link 5 GF(5) 155 Std Details Char Ring Dimension ID Generators Description Link 7 GF(7) 155 Std Details Char Ring Dimension ID Generators Description Link 11 GF(11) 155 Std Details Char Ring Dimension ID Generators Description Link 17 GF(17) 155 Std Details Char Ring Dimension ID Generators Description Link 31 GF(31) 155 Std Details