Dear forum, I am trying to compute among the class 2 groups of order 2^7 which ones admit a non-inner automorphism of order 2 that fixes the Frattini subgroup elementwise. I tried to check it manually before writing a code:
gap> LoadPackage("autpgrp"); true gap> all:=AllSmallGroups(2^7);; gap> lst:=Filtered(all,g->NilpotencyClassOfGroup(g)=2);; Length(lst); 947 gap> g:=lst[1]; <pc group of size 128 with 7 generators> gap> AutomorphismGroup(g); <group of size 6144 with 12 generators> gap> A := AutomorphismGroupPGroup(g);; gap> B:=PcGroupAutPGroup(A); <pc group of size 6144 with 12 generators> gap> I:=InnerAutGroupPGroup(B); Group([ f4, f3, <identity> of ..., <identity> of ..., <identity> of ..., <identity> of ..., <identity> of ... ]) gap> elmsg:=Elements(g);; gap> elmsaut:=Elements(B);; gap> elmsinn:=Elements(I);; gap> elmsaut0:=Difference(elmsaut,elmsinn);; gap> elmsaut02:=Filtered(elmsaut0,y->Order(y)=2);; gap> Fratg:=FrattiniSubgroup(g); Group([ f3, f4, f5, f6, f7 ]) gap> elmsFratg:=Elements(Fratg);; gap> a1:=elmsaut0[1];x1:=elmsFratg[1]; f1 <identity> of ... gap> a1(x1); Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `CallFuncList' on 2 arguments at /Users/sidhu/Desktop/GAP/gap-4.10.2/lib/methsel2.g:250 called from <function "HANDLE_METHOD_NOT_FOUND">( <arguments> ) called from read-eval loop at *stdin*:21 type 'quit;' to quit to outer loop brk> quit; gap> KnownAttributesOfObject(a1); [ ] gap> KnownAttributesOfObject(x1); [ ] i.e., GAP store the elements of automorphisms as plain list without knowing what it does to the elements of the group. What is a better option? Best regards, Siddhartha _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum