Order = 10151968619520 = 2^{10}.3^{12}.5.7.13.41.

Mult = 2.

Out = 2 × 2.

## Porting notes

Porting incomplete.## Standard generators

Standard generators of O_{8}^{−}(3) are *a*, *b* where *a* is in class 2A, *b* is in class 4F, *a**b* has order 41, *a**b**b* has order 6 and *a**b**a**b**b* has order 41.

Standard generators of 2.O_{8}^{−}(3) are preimages *A*, *B* where *A**B* has order 41 and *A**B**A**B**B* has order 41.

Standard generators of O_{8}^{−}(3):2_{1} are *c*, *d* where *c* is in class 2D/E, *d* is in class 8F, *c**d* has order 41, *c**d**d* has order 12 and *c**d**c**d**d* has order 18.

Standard generators of 2.O_{8}^{−}(3):2_{1} are preimages *C*, *D* where *C* has order 2 and *C**D* has order 41.

Type I standard generators of O_{8}^{−}(3).2_{3} are *g*, *h* where *g* is in class 3A, *h* is in class 8VW, *g**h* has order 56 and *g**h**h* has order 36.

Type II standard generators of O_{8}^{−}(3).2_{3} are *g*, *h* where *g* is in class 2A, *h* is in class 8XY, *g**h* has order 24, *g**h**h* has order 7, *g**h**h**h* has order 56 and *g**h**h**h**h* has order 3.

Standard generators of O_{8}^{−}(3).2^{2} are *i*, *j* where *i* is in class 2DE, *j* is in class 8B1, *i**j* has order 82 and *i**j**j* has order 8.

## Representations

### Representations of O_{8}^{−}(3)

- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 1066 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 246 Std Details 3 GF(3) 8 Std Details

### Representations of 2.O_{8}^{−}(3)

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- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(9) 8 a Std Details 3 GF(9) 8 b Std Details 3 GF(3) 16 Std Details

### Representations of O_{8}^{−}(3):2_{1}

- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 1066 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 8 Std Details

### Representations of 2.O_{8}^{−}(3):2_{1}

- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 16 Std Details

### Representations of O_{8}^{−}(3).2_{3}

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- Permutation representations:
Number of points ID Generators Description Link 1066 Type I Details 1066 Type II Details - Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 8 a Type I Details

### Representations of O_{8}^{−}(3).2^{2}

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- Permutation representations:
Number of points ID Generators Description Link 1066 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 16 Std Details

### Representations of O_{8}^{−}(3).D_{8}

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- Matrix representations
Char Ring Dimension ID Generators Description Link 3 GF(3) 8 Details