How to iterate over groups in increasing size

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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)]
...