In GAPthere are various databases available for groups, see http://www.gap-system.org/Datalib/dat...

Some of them are interfaced in Sage and available in the database_gap package. So first of all you have to install the package with the console command (needs internet connection)

```
$ sage -i database_gap
```

Then if you launch Sage you should be able to do

```
sage: for G in TransitiveGroups():
....: print G
....: print G.gens()
Transitive group number 1 of degree 0
[()]
Transitive group number 1 of degree 1
[()]
Transitive group number 1 of degree 2
[(1,2)]
Transitive group number 1 of degree 3
[(1,2,3)]
Transitive group number 2 of degree 3
[(1,2), (1,2,3)]
Transitive group number 1 of degree 4
[(1,2,3,4)]
...
```