`IsSpecialPcgs` for pcgs of solvable small groups?

[ThomasBreuer]

It seems that Pcgs( G ) = SpecialPcgs( G ) holds for solvable G from the small groups library.
If this is true in general then shouldn't IsSpecialPcgs be set to true in Pcgs( G )?

[fingolfin]

Perhaps it is true (it would make a lot of sense), but we should verify that before setting it unconditionally.

Perhaps @beick remembers?

Otherwise, what I'd suggest to do (for "someone" who has time and interest to improve this) is to go through each layer, verify this for all the groups in that layer, and then ensure that the this property is set for the constructed groups in each case. Typically that means searching for the calls to PcGroupCode resp. PcGroupFpGroup and then modifying those call sites suitably.

Note that there are other things that could be set. E.g. we call SetIsPGroup and SetPrimePGroup in some cases constructing p-groups, but not all. We could potentially set information about being nilpotent, solvable, non-solvable (basically: whenever we set a permutation group).