Order = 3265920 = 2^{7}.3^{6}.5.7.

Mult = 3 × 3 × 4.

Out = D_{8}.

## Porting notes

Porting incomplete. This group has a lot of problems. Might have to copy over by hand.## Standard generators

Standard generators of U_{4}(3) are *a*,
*b* where *a* has order 2, *b* is in class 6A,
*a**b* has order 7 and
*a**b**a**b**a**b**b**a**b**a**b**b*
has order 5.

Standard generators of U_{4}(3).2_{1} are
*c*, *d* where *c* is in class 2B, *d* has
order 9, *c**d* has order 14 and
*c**d**c**d**d* has order 9.

Standard generators of U_{4}(3).4 are *e*,
*f* where *e* is in class 4E/E', *f* has order
9, *e**f* has order 28 and
*e**f**e**f**f* has order 6.

Standard generators of U_{4}(3).2_{2} are
*g*, *h* where *g* is in class 2D, *h* has
order 7 and *g**h* has order 8.

Standard generators of U_{4}(3).2_{3} are
*i*, *j* where *i* is in class 2F, *j* has
order 5, *i**j* has order 8, *i**j**j*
has order 8, *i**j**i**j**j* has order
7 and
*i**j**i**j**j**i**j**j**j*
has order 10.

Standard generators of
3_{2}.U_{4}(3).2_{3} are preimages
*I*, *J* where *I* has order 2 and *J* has
order 5.

Standard generators of
3_{2}.U_{4}(3).2_{3}' are preimages
*I*, *J* where *J* has order 5.

Standard generators of U_{4}(3):D_{8} are
*o*, *p* where *o* is in class 2DD', *p* is
in class 6NN' and *o**p* has order 20.

Standard generators of 2.U_{4}(3).D_{8} are
preimages *O*, *P*.

## Representations

### Representations of
U_{4}(3)

- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 21 Std Details 0 Z 35 a Std Details 0 Z 35 b Std Details 0 Z 90 Std Details 0 Z 140 Std Details 0 Z 189 Std Details 0 Z 210 Std Details

### Representations of
U_{4}(3):D_{8}

- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 112 Std Details 252 Std Details 280 Std Details 324 Std Details 540 Std Details 1134 Std Details 2835 Std Details 4536 Std Details 5184 Std Details 8505 Std Details 9072 Std Details

### Representations of
3^{2}.U_{4}(3):D_{8}

- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 756 a Details 756 b Details 972 Details

### Representations of
2.U_{4}(3).D_{8}

- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 6 Std Details