Order = 227787103272960 = 2^{21}.3^{8}.5.7.11.43.
Mult = 1.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of U_{7}(2) are a, b where a is in class 2A, b has order 7, ab has order 33 and abb has order 45.
Presentations
Group | Presentation | Link |
---|---|---|
U_{7}(2) | 〈 a, b | a^{2} = b^{7} = (ab)^{33} = [a, b]^{3} = [a, b^{2}]^{3} = [a, b^{3}]^{3} = [a, bab]^{2} = [a, b^{2}ab^{2}]^{2} = [a, bab^{2}]^{3} = (abab^{−3}ab^{−3})^{8} = 1 〉 | Details |
Representations
Representations of U_{7}(2)
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 2709 Std Details 2752 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 2 GF(4) 7 a Std Details 2 GF(4) 7 b Std Details
Maximal subgroups
Maximal subgroups of U_{7}(2)
Subgroup | Order | Index | Programs/reps |
---|---|---|---|
2^{1+10}:(3 × U_{5}(2)) | Program: Generators | ||
3.U_{6}(2).3 | Program: Generators | ||
2^{9+6}:3.L_{3}(4).3 | |||
2^{4+12}.(A_{5} × 3^{1+2}:2A_{4}) | |||
3 × S_{3} × U_{5}(2) | |||
3^{1+2}:2A_{4} × U_{4}(2) | |||
3^{6}:S_{7} | Program: Generators | ||
43:7 = F_{301} |