Order = 6065280 = 2^{7}.3^{6}.5.13.

Mult = 2.

Out = 2 × 2.

## Porting notes

Porting incomplete.## Standard generators

Standard generators of L_{4}(3) are *a*,
*b* where *a* is in class 2A, *b* is in class
4B, *a**b* has order 13 (necessarily in class 13A/B)
and *a**b**b* 8. Alternatively: *a* is in class 2A, *b*
is in class 4B, *a**b* has order 13 (necessarily in
class 13A/B) and *a**b**a**b**b* has
order 13.

Standard generators of 2.L_{4}(3) are preimages
*A*, *B* where *A**B* has order 13 and
*A**B**A**B**B* has order 13.

Standard generators of L_{4}(3).2_{1} are
*c*, *d* where *c* is in class 2C, *d* has
order 5, *c**d* has order 26 and
*c**d**c**d**d* has order 5.

Standard generators of 2.L_{4}(3).2_{1} are
preimages *C*, *D* where *D* has order 5.

## Black box algorithms

### Checking generators (semi-presentations)

Group | Semi-presentation | File |
---|---|---|

L_{4}(3) |
〈〈 a, b | some
conditions 〉〉 |
Download |