alexander konovalov's profile - activity

No, AllSmallGroups(64); in GAP works perfectly fine.

\in is membership test. Another form of calling it would be \in( Identity(G), G );. It does not matter in this example what is G, but if you need something for the test, try e.g.\in((1,2),SymmetricGroup(3));.

To me, the error message hints that one tries to call RankPGroup on a group which is not a $p$-group. I don't know why SageMath attempts this though.

Looks to me like the call G.orbit(Set(K[0]), action = "OnChains") is a Sage command which refers to some Sage to GAP interface, which implements only support for standard types of actions. If you want to use own OnChains action, you may have to make a direct call of a GAP command (e.g. Orbit(G, Set(K[0]), OnChains);) instead of using the Sage interface.

GAP 4.7.7 (February 2015) fixed a bug where recursive records might be printed with the wrong component name, coming from component names being ordered differently in two different pieces of code (see here). Could this be related? Is this reproducible with GAP 4.7.7 or 4.7.8?

@Amri in GAP, you can iterate over all groups of a given order (if Small Group Library provides them) - see SmallGroup and NrSmallGroups. Then you may use Image(IsomorphismPermGroup(G)) on the GAP side to get a permutation group before importing it into Sage.

There is probably a typo in the question, not in what you've really tried - in `gap.eval('SmallGroups(8,1)')` one should use "SmallGroup" without trailing 's'