Order = 3732063900024176640 = 235.38.5.7.11.43.
Mult = 1.
Out = 2.
Porting notes
Porting incomplete.Standard generators
Standard generators of 214.U7(2) are a, b where a is in class 2C, b has order 7 and ab has order 33.
Notes
- (214.U7(2)) 214.U7(2) has a unique conjugacy class of subgroups of index 10836, and we may take a to be a central involution in such a subgroup. In fact, this subgroup turns out to be C(a). Also, a happens to be in a class of 3-transpositions, and a commutes with 2644 of its conjugates. The orbits of C(a) (acting by conjugation) on the conjugates of a have sizes 1, 3, 2640 and 8192.
- (214.U7(2)) No extra conditions (such as abb having order 45) are required. These generators map onto standard generators of U7(2).
Presentations
| Group | Presentation | Link |
|---|---|---|
| 214.U7(2) | 〈 a, b | a2 = b7 = (ab)33 = [a,b]3 = [a,b2]3 = [a,b3]3 = [a,bab]2 = [a,b2ab2]2 = [a,bab2]3 = (abab3abab−2ab−2)6 = 1 〉 | Details |
Representations
Representations of 214.U7(2)
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 10836 Std Details
Miscellaneous Notes
| Group | Category | Note |
|---|---|---|
| 214.U7(2) | Bibliographic reference. | As far as we know, this group was discovered by J.I.Hall. He also discovered its 3-transposition property. |