p:=◯;;n:=◯;;order:=p n;; # Input the values of p and n, where the order of G is p n | G:=AllSmallGroups(Size,order);; | D:=NumberSmallGroups(order);; | for k in [1..D] do; | f:=G[k];;x:=Elements(f);;YY:=Collected(List(x,i-[Order(i)]));; | m:=Size(MinimalGeneratingSet(f));; | if NilpotencyClassOfGroup(f)=2 and m=2 then; | Print(k,") |G|=",Size(f)," p=",p," n=",n," N.class ",NilpotencyClassOfGroup(f), | gg:=MinimalGeneratingSet(f);; | e:=Identity(f);; | a:=gg[1];;b:=gg[2];;c:=Comm(a,b);; | i:=Log(Order(a),p);;j:=Log(Order(b),p);;w:=Maximum(i,j);; | Print("∖n no. of gen.=",m,", o(a)=",Order(a),", o(b)=",Order(b),",w=",w,"∖n | OC=",YY,"∖n∖n"); | fi;od;time; |
|