The Order Classes of 2-Generator -Groups

Algorithm 2

The ordinary GAP algorithm.

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;