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,
*a**b* has order 33 and *a**b**b* 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} |