Zmn:=function(m,n) F:=FreeGroup(2);;G:=F/[F.1^4,F.2^4,(F.1^m*F.2^m)^n,F.1^(-1)*F.2*F.1^(-1)*F.2];;return G;end;;
該有限羣序列有4個伴隨的有限羣序列：
中心序列：
ZZmn:=function(m,n) return Center(Zmn(m,n));end;;
換位子羣序列：
DZmn:=function(m,n) return DerivedSubgroup(Zmn(m,n));end;;
射影中心序列：
PZZmn:=function(m,n) G:=Zmn(m,n);return G/Center(G);end;;
射影換位子羣序列：
PDZmn:=function(m,n) G:=Zmn(m,n);return G/DerivedSubgroup(G);end;;
for n in [1..7] do Print(IdGroup(Zmn(1,n)),IdGroup(Zmn(2,n)),"\n");od;for n in [8] do Print(IdGroup(Zmn(1,n)),Size(Zmn(2,n)),"\n");od;for n in [9..15] do Print(IdGroup(Zmn(1,n)),IdGroup(Zmn(2,n)),"\n");od;
Fun:=ZZmn;;for n in [1..7] do Print(IdGroup(Fun(1,n)),IdGroup(Fun(2,n)),"\n");od;for n in [8] do Print(IdGroup(Fun(1,n)),Size(Fun(2,n)),"\n");od;for n in [9..15] do Print(IdGroup(Fun(1,n)),IdGroup(Fun(2,n)),"\n");od;
Fun:=DZmn;;for n in [1..7] do Print(IdGroup(Fun(1,n)),IdGroup(Fun(2,n)),"\n");od;for n in [8] do Print(IdGroup(Fun(1,n)),Size(Fun(2,n)),"\n");od;for n in [9..15] do Print(IdGroup(Fun(1,n)),IdGroup(Fun(2,n)),"\n");od;
Fun:=PZZmn;;for n in [1..7] do Print(IdGroup(Fun(1,n)),IdGroup(Fun(2,n)),"\n");od;for n in [8] do Print(IdGroup(Fun(1,n)),Size(Fun(2,n)),"\n");od;for n in [9..15] do Print(IdGroup(Fun(1,n)),IdGroup(Fun(2,n)),"\n");od;
Fun:=PDZmn;;for n in [1..7] do Print(IdGroup(Fun(1,n)),IdGroup(Fun(2,n)),"\n");od;for n in [8] do Print(IdGroup(Fun(1,n)),Size(Fun(2,n)),"\n");od;for n in [9..15] do Print(IdGroup(Fun(1,n)),IdGroup(Fun(2,n)),"\n");od;
又如H_16n=<a,b|a^4n=b^4=1,ab=ba^-1>的4個伴隨有限羣序列：
H16n:=function(n) F:=FreeGroup(2);;G:=F/[F.1^(4*n),F.2^4,F.1*F.2*(F.2*F.1^(-1))^(-1)];;return G;end;;
ZH16n:=function(n) return Center(H16n(n));end;;
DH16n:=function(n) return DerivedSubgroup(H16n(n));end;;
PZH16n:=function(n) G:=H16n(n);return G/Center(G);end;;
PDH16n:=function(n) G:=H16n(n);return G/DerivedSubgroup(G);end;;
Fun:=H16n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;
Fun:=ZH16n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;
Fun:=DH16n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;
Fun:=PZH16n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;
Fun:=PDH16n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;
其中，ZH16n≡GAP[4,2],PZH16n=DihedralGroup(4n),DH16n=CyclicGroup(2n),PDH16n≡GAP[8,2]
Q4n:=function(n) F:=FreeGroup(2);;G:=F/[F.1^(2*n),F.2^2*F.1^(-n),F.2^(-1)*F.1*F.2*F.1];;return G;end;;
ZQ4n:=function(n) return Center(Q4n(n));end;;
DQ4n:=function(n) return DerivedSubgroup(Q4n(n));end;;
PZQ4n:=function(n) G:=Q4n(n);return G/Center(G);end;;
PDQ4n:=function(n) G:=Q4n(n);return G/DerivedSubgroup(G);end;;
Fun:=Q4n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;
Fun:=ZQ4n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;
Fun:=DQ4n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;
Fun:=PZQ4n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;
Fun:=PDQ4n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;
M_8n=<a,b|a^4n=b^2=1,bab^-1=a^(2n+1)>
M8n:=function(n) F:=FreeGroup(2);;G:=F/[F.1^(4*n),F.2^2,F.2*F.1*F.2*F.1^(-1-2*n)];;return G;end;;
ZM8n:=function(n) return Center(M8n(n));end;;
DM8n:=function(n) return DerivedSubgroup(M8n(n));end;;
PZM8n:=function(n) G:=M8n(n);return G/Center(G);end;;
PDM8n:=function(n) G:=M8n(n);return G/DerivedSubgroup(G);end;;
Fun:=M8n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;
Fun:=ZM8n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;
Fun:=DM8n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;
Fun:=PZM8n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;
Fun:=PDM8n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;
U6n:=function(n) F:=FreeGroup(2);;G:=F/[F.1^3,F.2^(2*n),F.1*F.2*F.1*F.2^(-1)];;return G;end;;
ZU6n:=function(n) return Center(U6n(n));end;;
DU6n:=function(n) return DerivedSubgroup(U6n(n));end;;
PZU6n:=function(n) G:=U6n(n);return G/Center(G);end;;
PDU6n:=function(n) G:=U6n(n);return G/DerivedSubgroup(G);end;;
Fun:=U6n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;
Fun:=ZU6n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;
Fun:=DU6n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;
Fun:=PZU6n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;
Fun:=PDU6n;;for n in [1..31] do Print(IdGroup(Fun(n)),"\n");od;