Order = 319979520 = 215.32.5.7.31.
Mult = 1.
Out = 1.
Porting notes
Porting complete, but handling of notes is unsatisfactory.Standard generators
Standard generators of 25.L5(2) are a, b where a has order 2, b has order 5, ab has order 21, ababb has order 10, abababbbb has order 28 and abababbbabb has order 5.
Notes
- (25.L5(2)) These generators map onto standard generators of L5(2).
Presentations
| Group | Presentation | Link |
|---|---|---|
| 25.L5(2) | 〈 a, b | a2 = b5 = (ab)21 = [a,b2]4 = [a,b−2ab−2][a,b]3 = (ababab−2)2(abab−1ab)2(ab−1)2 = 1 〉 | Details |
Representations
Representations of 25.L5(2)
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 7440 a Std Details 7440 b Std Details 7440 c Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 248 Std Details 2 GF(2) 69 a Std Details 3 GF(3) 248 Std Details 5 GF(5) 248 Std Details 7 GF(7) 248 Std Details 31 GF(31) 248 Std Details
Miscellaneous Notes
| Group | Category | Note |
|---|---|---|
| 25.L5(2) | Group theoretic trivia. | There is just one class of involutions of 25.L5(2) not in the normal 25 and it maps onto class 2A of L5(2). |