FinalCode.sagews

def givequotients(i,j):
    mygroup = gap.SmallGroup(i,j)
    mysubgps = gap.NormalSubgroups(mygroup)
    for k in range (1,len(mysubgps) + 1):
        myquotient = gap.FactorGroup(mygroup,mysubgps[k])
        print gap.StructureDescription(myquotient)



def findgroups(lower,upper):

    for i in range(lower,upper + 1):
        numbergroups = gap.NumberSmallGroups(i)
        for j in range(1,numbergroups + 1):
            mygroup = gap.SmallGroup(i,j)
            quotientFlag=True
            #print '---------'

            if not gap.IsAbelian(mygroup):
                mysubgps = gap.NormalSubgroups(mygroup)
                for k in range(2,len(mysubgps)):
                    myquotient = gap.FactorGroup(mygroup,mysubgps[k])

                    if not gap.IsAbelian(myquotient):
                        quotientFlag = False
                        break
                if quotientFlag == true:
                    print gap.StructureDescription(mygroup) , " - GAP Group ID:" , (i,j)

#findgroups(1,60)p.StructureDescription(gap.SmallGroup(16,2))



findgroups(1,10)

C4 x C4 S3 - GAP Group ID: (6, 1) D8 - GAP Group ID: (8, 3) Q8 - GAP Group ID: (8, 4) D10 - GAP Group ID: (10, 1)

givequotients(6,1)

S3 C2 1

done":true}

givequotients(6,1)

S3 C2 1