Order = 174182400 = 2^{12}.3^{5}.5^{2}.7.

Mult = 2 × 2.

Out = S_{3}.

## Porting notes

Porting incomplete. Needs attention. Standard generators have many comments.## Standard generators

Standard generators of O_{8}^{+}(2) are *a*, *b* where *a* is in class 2E, *b* is in class 5A, *a**b* is in class 12F/G and *a**b**a**b**a**b**a**b**b**a**b**a**b**b**a**b**b* has order 8. Alternatively: *a* has order 2, *b* has order 5, *a**b* has order 12, *a**b**b* has order 15 and *a**b**a**b**a**b**a**b**b**a**b**a**b**b**a**b**b* has order 8.

Standard generators of 2.O_{8}^{+}(2) are preimages *A*, *B* where *B* has order 5, *A**B**B* has order 15 and *B* is in class +5A. Alternatively: *B* has order 5, *A**B**B* has order 15 and *A**B**A**B**B* has order 15.

Standard generators of 2^{2}.O_{8}^{+}(2) are preimages *A*, *B* where *B* has order 5 and *A**B**B* has order 15.

Standard generators of O_{8}^{+}(2):2 are *c*, *d* where *c* is in class 2F, *d* is in class 10BC and *c**d* has order 18. Alternatively: *c* is in class 2F, *d* has order 10, *c**d* has order 18 and *c**d**d* has order 30.

Standard generators of 2.O_{8}^{+}(2).2 are preimages *C*, *D* where *C**D*(*C**D*^{4})^{3} has order 3.

## Presentations

Group | Presentation | Link |
---|---|---|

O_{8}^{+}(2):2
| 〈 c, d | c^{2} = d^{10} = (cd)^{18} = [c,d]^{2} = [c,d^{2}]^{2} = [c,d^{5}]^{4} = [c,d^{3}]^{3} = [c,d^{4}]^{3} = (cd^{2})^{2}(cd^{4})^{2}cd^{2}(cd^{−4})^{2}cd^{4} = (cd^{3}cd^{4})^{7} = 1 〉
| Details |

## Representations

### Representations of O_{8}^{+}(2)

- View detailed report.
- Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 28 Std Details 0 Z 35 a Std Details 0 Z 35 b Std Details 0 Z 35 c Std Details 0 Z 50 Std Details 0 Z 84 a Std Details 0 Z 84 b Std Details 0 Z 84 c Std Details 0 Z 175 Std Details 0 Z 210 Std Details 0 Z 210 a Std Details 0 Z 210 b Std Details 0 Z 210 c Std Details