gap> grp(18);

Group 1 has structure: D18 and is Non-Abelian

Group 2 has structure: C18 and is Abelian

Group 3 has structure: C3 x S3 and is Non-Abelian

Group 4 has structure: (C3 x C3) : C2 and is Non-Abelian

Group 5 has structure: C6 x C3 and is Abelian

The workhorse here is the function ConstructAllGroups and is part of the GAP package GrpConst.

#

# Prints all groups of order n

# IN: Group

#

grp:=function(n)

local listGroups;

listGroups:=ConstructAllGroups(n);

i:=1;

while(i<(Length(listGroups)+1)) do

Print("Group ");

Print(i);

Print(" has structure: ");

Print(StructureDescription(listGroups[i]));

Print(" and is ");

if (IsAbelian(listGroups[i])) then

Print("Abelian");

else

Print("Non-Abelian");

fi;

Print("\n");

i:=i+1;

od;

end;

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