Order = 319979520 = 2^{15}.3^{2}.5.7.31.
Mult = 1.
Out = 1.
Porting notes
Porting complete, but handling of notes is unsatisfactory.Standard generators
Standard generators of 2^{5}.L_{5}(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
- (2^{5}.L_{5}(2)) These generators map onto standard generators of L_{5}(2).
Presentations
Group | Presentation | Link |
---|---|---|
2^{5}.L_{5}(2) | 〈 a, b | a^{2} = b^{5} = (ab)^{21} = [a,b^{2}]^{4} = [a,b^{−2}ab^{−2}][a,b]^{3} = (ababab^{−2})^{2}(abab^{−1}ab)^{2}(ab^{−1})^{2} = 1 〉 | Details |
Representations
Representations of 2^{5}.L_{5}(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 |
---|---|---|
2^{5}.L_{5}(2) | Group theoretic trivia. | There is just one class of involutions of 2^{5}.L_{5}(2) not in the normal 2^{5} and it maps onto class 2A of L_{5}(2). |