Details Page for 0.3352

Complete Solution is Known:

MSV File: q-0.3352.msv

Growth Pattern:

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Details for Q₁₇₆₇(0.3352):

Q = <a,b,c,d,e,f,g | a²=1, b³=b, b²c=c, c²=b², b²d=d, d²=b², b²e=e, e²=b², b²f=f, f²=b², b²g=g, g²=b²>

P = {a, b²}

Phi = 1 a b ab b² b ab² c b ab² c b b² ab b ab² ab ac c b ac ab bc ab² b bc b² b ab² ac ab ab² abc d b² ab ab² c ab ac c b b² ab d ab² ab ac bd b c ab bc ab² b d b² b ab² bd ab ab² c abc b² ab ab² c ab ac bd b c bd d ab² b d ac b ab² ab bc ab² abc d b² ab b bd ab ac c ab² b² ab ab² c b ac bd b ab² bd b² ab² abc d ab abc ab² ab bc ac b abc b² ab c b bc ac bd abc c bc b² ab² abc d bc abc ab² bd ab ac abc d b² ab c bd bc ac bd c ab² ab d ab² abc ac bd abc ab² bc b² bd abc d ac ab ab² bd bc ac abc ab² b² ab c b d ac bd abc ab² ab b² ab² abc ac ab d ab² bc b² bd abc ab² ac ab ab² abc ad ac abc ab² abd ab b² bd d ac bc abc ab² ab ac bd abc cd b² ad ab² abc bc bd abc ab² abd ab e abc ad ac bc ab² c ab ac bd ad ac b² ad ab² abc ac abd abc c bd ab ab² abc d ac bc b abd ab ac bd ad ac bc d ab² ab ac bd abc ab² b² ab ab² abc d bd b c bd ab e bd abc ac bc cd ab² ab ac bd d ac b² d ab² abc ad ac abc c bcd ab e abc d bd bc c bd ab ac abcd c ab² bc ad ab² abc ac bd abc e bc d c abc acd ac ab c abd ab ac abc c ac be e ab² ab ac abcd c e bc cd ab² be e ac ad e bcd ab e abc c ac ad c b ab e be c abd bc cd ab² be ac ab b e bc ac abcd ab² e bd ab e bcd ab abcd abc c bcd ad e bd be e bd b bcd be ac c be ac bc ad e be ab abcd abc c ac cd c bcd ab bc be b abd d ac c acd ac abcd cd abc be bc bcd be c ac ad e abe d abcd abc ae bcd ad e c ad ce abe b abd ab e bd ab² c bd acd abd be cd abd bce ae abd ad ab² abe d ab be b ab² cd ad c d e abcd ad abc be e bd be ae bd ab ace be de b² ab ae bd ac e c d ae be ace ab² bce ab abe c e bd d abd be ae bc abce e bcd b² e c d abcd be ae bd ad ae ade ad abd be cde bd abe e bd acd ae be b² ace abe de ac bce b bcd ad ce be abc abde abe e abd abce ab bce d ce be bc bd bce e ac ade b bce ab bde be ae abcd bce ae c acd ab be abc ce abe ace bd be e bd d abd be bc abcd c ae b² bce e abde bc bde abe abc bde abe e c acd ae bce cd abd be ace bcd acd ae ac cd ace be bc bde abe ce b² ac e c acd ab bce abc abde abce ace bcd ad e abce ade abc be ab bde ab² ce b² ab e abce bc bd be ace bde ac e ab² abc ab bce d abd be ad bde ab² ae bce ab abc be bc ac de ce abde ad bde ab² de ab bce ace ab² abce ab abe b bde ac ade abc abce bc ac abce ce bcde ab ace bce ae abd abe abc abce de ace bce abc abde bce cde ab² abce ab ac c abde abce ade bde abce ce abcd abe abc bcde d ace ab² abc bd ade ace c de ce f abc abde abce bc bcd acde ce ac ade abde f bc bde ab² acde ab ade ce c de bde ade abc bd de ce c d ce abcde b ab² bce bc bde de bcde abcd ade bcde f ade e cde d ac ade ce c de ab cde abc abde abce ace abcde de ce f cde abde de bc bde de ce bd bc ace c acde ab f abc bcd de ace c abc ab bce ade abde bce bc c ab² abde ac ade bde de cd b² ade ace abde bc abcde c de bde bce ace c de bf f abc abde f ade c acde cd ac ade bf bd bc bde f bf bde ade ace abde ac abcde f abc bcde f cd ab² de bf f de abde bd bc bde de bf abcd ade bf bcde de abcde f bf abde bce bf c de abcde bd ab² abde f cde bde acde cd abcd ade bcde f acde bde f d bc ade ace c de abcde f acd abde cde bf bcde de bf bde cde abde f cde bde de bf abcde ade bf f acde abcde f acde bd ade bf bd de bde f ab² abde af cd bde de bf bd ade abde f d bde cde d af ade abf bcd de bde f bf bcde cde bf af de bf bde abf abde acde cd bde de bf f ade bcf f abf bde f bf af ade abf f de bde f abf abde acde ad bde abc abde f ade ab² af bf bde de bf af ade abcde abd de ac ade bf af ade bf bd de bcde f abf bde de bf abcd de abde f cd bde acde cd bde cde acd bcd de bde f de bde cde abf abde de bf ace c bcde af bce bde acde bf bde de acd af cd bde cf abce bc ade abf abde de bde f abce abde ade bce abde de bcf ace ade abd af ade bde cf abce ab bdf abde af de bde cf de abde ad abf abde de bde abcde abf abde cf bce abcde bdf bf abcd cde abcf cf ac bde cf bf bd ab abf ace de bde f bcf bcde bdf abf af bdf bcf ace ade ab² af bce bde de abce cf cde bcf f abcf ac f bce abde ade bf ace abcf bde abcd abcf abde ae bf acf acd be bd abe abde de abce bde acf abce af ade bcf f abce abcd f bce abde bdf ade cf bdf abcf abcde abf abde ae bce abcd de bf ce abe bde af cd df ade bce ae bdf abe ce c bde ce bce bcd de abce ace bdf df ce bce df cf bce ace ade bce ce cd abf ce be abcd e abce abc de bf e abdf bf ce abe df bdf abe acf bdf be ace ac bde af be abcd bdf be bcde cd bde acf be df e abe df de abe e bdf df ace b² bcd bdf be bc bdf adf ce bdf bd abdf be df bdf bce bcd cd bd e c df abdf abe df af adf bd d abd ae abe df bdf be af bce adf ce bdf df ace be df bdf abe e bdf bd e abdf abd bdf abe adf d be bc bdf df ae be ab abdf be adf ad bef ce cd df e c abc bdf abe ce ab² be e abcdf abd ce abe abd abdf be e ac adf e be bc bdf be bd ad bce e b adf e be ab² abdf be ace ac be e bcdf abd ce be bc abdf be ae ad abe e be bd abcdf be bcd bdf abe e d adf e bef bcd abdf be bd abdf abce e cd df d be abcd bdf be bcd ad adf e d df ace be abd bdf bce e d be e bce abc bdf be abcd bdf abce ae cd df ef d adf bcf abe bcd bdf df e b df ef abe aef bdf be bd d abd ae bc df d be bd ac adf ae abcdf abcd e abce bd ad abe ae bdf adf e acf df ce abe cdf d be abcd bdf abce ae bef abcd abdf be acdf ad bce ae ad adf e be df bcdf abe bcd acd de e cd abd ce abe abd abdf be e ad adf ae cf bd bcdf be bd ad abe ae acd adf e be abd bcdf bce e d be e abcdf abd ae abe abcd bde abce ae ad bce c abef bd ace abc abd bcdf abe ab² d de ce bce ab² c bce ef d de ce ab bcf abde be ac bde bce ef bcdf adf e b de ac f ab² cf abe aef d de ae ab df ae be ac abdf de abde ad bce ef abef abcf ace abe bcd bdf bd ace abc df cef abef ef ce abce ac bdf abce ac ab bcf bdf abce ac bdf bce c bef bce c d abcf abcde abe bf bdf adf ace d bf ef abe abd acef be ac f cdf c acf adf abdf abc ac ad bce abf af ade ace abc abcf abcdf bc bf abc abcef ac f adf ae af bcf acef abce ac acf def c abc df cef abc abcf aef abe bf abc adf ac f abcf acef bc abf d be ac ad df c ab bcf cef abc bf abcde cde ef af bcf ace abc abd bdef abe abd abc cde ac f bf ab² cf ac abdf abc ac bc def ce ab cdf ace abc bf abcdf ab bcf abc cdf ac acf c bdef bc ab² bdef b ac f acdf ae abc ac bdef abc abcf acf def c abc def b² g abcf bdef ade c abc def bde af abcf ce acde ac bdef abef ac bc def bcde af bcf e abef abd bdf abe aef abc def cef ab c ce ade bde abc abce bf bc def ce abc ac ace acde acef bc abe ef abc bf e cde c cf abcef bd abc abcf bdef abcef bf ce be ac bdef def bcde bc def bdef abc ac e abef abd acf bce abf abc be aef bce bcf abc def ac abc be abdef af abe bdef af abf f abef ae bc ac ef abc acdef f bcef abcf cf bef e cf abce ef abe c ef def ac bcdf def abdef bc bcf acef be bcf bdef bef bcdef bc bef abcdef abc abcf cef abe abcf cf def e bc abcf acef g bcf acef def ac acf def ae bc ac bdef g ac bdf abef abcf abc def e abc abcf ef acf ac bdf cf ac g abcf ce acdef ac bdef abc ac bc def bdef g ac e abc bf abdef abe ac cf def e f g ce adef abcde bdef be bcdef cf adef ae g bcf bdef adef abde cf bce abdef cf def acf g abcf abdef adef abcde cf abef abdef abe adef ae ad ace bdef def abcf cf adef abd acde bcf acf be abde abdef abe abcdef ae def bdef g abg bdef ad bde abcdef abef bcde bdf adef abd be g bdef def ce cg bef abd abcdf acdef acf adef abcf abdef def e abc abef abd bce g ef abcef abg abcdef bef abdef af bef bdef be bcg aef cdef bcg cg bef bcg acg abcef aef bcdf bf ef ad e cg abef abdef cg bcef abd be abcg cef bef ce cg bef ef bcde cdf abcdef adef acdf ef acdef e cg bcef abd cd bcg abcdf acdef ac g acd abdef abcdf bef bdef be cdf aef bef ce cg cd bdef acg df cef abe acdf ef def e cg acd bcd ag bcg ef be abg acf bef bcd cg df ef acd ce acef ad acdf ef bef abcd acg bcg abcdef cd abf ef bef abcd g cdef ae abcdf abcef abcd be bcd bcdf cd bcd bcde abcef e acd bg ag bce acdf acef acd ace g bcef cf cd ace abcdef acdef bg g abf abcdef cd abcef abcd acd de abdef bc bcd be bcef e cg adf ef abdg abcd cg acd e abe adef ae cd e aef abc abde aef cd dg be abef e abdg ae ef acdef bcd abce abef ac ade bg ef cd bg g bcef bg abe bcg c ag abcef ef abdg ce g abef abg g abcef cef cd bg ef bef ace g bef dg cd bg acef ag bg ef cdef bcd cg cde dg abce bg aef abdg ae bcde abcef abg ef bef bcdef abe bcg ef bc ace bce abef bg bce ace bcdf be bcg ef abef ae cg bef bde abce ae cef cd bg bcde bef ace g abef dg abe ace ef abdg bg bce bcef ae g bef dg g ce ef bc ae abce bef abcd g ce cef abe bcg ef abc e bce abef c abe ace ef b dg bdf bc ae abce bef dg cg bcef cef abe bcg abce de ace g abef c abe ace ef cf abcg abe abef abde cg ace ef bdg ae aef bdg dg abce bef f bdg ae abde ade abcg abce de dg abe abef cef ab ace acef abc adg abe ade dg de bef c cde ae abdef ace dg acef de dg acg ae ef abdg abcde acef de bcde cg abcef abde de ace bde bdg bcde aef ace dg abce abcef bce abdg adef ef ade ace acef bdg ac cde abef abce abdg bcg bde bf bcde cg ace c abce bef bde bdg abde aef ace e abce de aef ade abef abce bef ace acef de abde ade bef ef abce def bde abef abde bcdef ade dg acg bef bde ade bcg abce ade abcde bdef de acdg ade abef abde de abcde ef de bcde ag ade ef acde def bde ade abde bcdef abcef bde acg bef acdg bce abef abde de abcde abcdef abef abde ade bcef cef acde def bde bc bcde bcdef abf bde abdg acdef aef ade adg bcdef bef adg ade abef abde ade cdef af abdg abcde ef bcg abde bcdef beg aeg acde abde aef ade abde aef abcef abcde abcdef abde cef ade cdef ef acde abcde cde abef abde ade ace ef acde cdg bcdef cdef abde bcdef def abcde acde bcde af cde dg acde bceg abcde aeg abef bcd ade abcde cf de abcde ade cd abde abdef bef abcd acg abde aef ade abde acde abcef bde ade abde bcd ade adg ef acd abcde cde abef abd acde abcde bdef d abde abdef cd acef acde bef ace ade bcde f ade bcde acde acd abcde cde cdef bcd cde abcde ef abce bcde ade abef cf acde abcde abcd abef abde f cd bcde acde abcef dg acg bcde bcdef cde abcde bdef bf dg cde abef bcd acde abcde acef bf abde cde cd dg acde bef abcd ade bcde aef bcdg abcde bdg acd acdg cde def bcd beg abcde acef abce abcg cde abcf af acde def bd abcdg bg aef ad af bdef abef bde cde def bcd abcef abcde bdef acd bg cde cdef eg ag bg bcdef abcf ce cde abcde bcg ag abcef bdef ade bcde bcdef bce ace bdg abcef eg bcf beg cf abeg abg abcdef def abde cde acdef af bf abcef ace d abcg abdef def f abcf abcef f bcf bcde abcdef abf abcd bcdg cdef abcg cde def abdef bf dg bdef abf abd bdeg abcef cf abce abcef aef ad bcde abdg acdef ace cde bcde af ad abg ce def abcg bcdg abef abd cde def cf d adg abdef acg abd aceg bef f g abcef aef ad cdg bdef bcf e bcdg def af ad beg acef be dg aeg abef abd abcdg adef f abce def aef abf af cef abcef ace bdg cdg bcdef abe abg acef abce ace bdef abef ce abeg beg ace abce bg bcdef abef abd eg bef ace acd abeg aef abe abg acef abce ace bf cdef bg bf adg acef be f abdg abef ae cg abceg ace de cf cef abe ce bcf bef e bf bcef ae abf af acef abce ace bcdg bcef ae abce bef ef be bg bcdg bcf ce cg acdef e bf cf cef abe af acd be ace bcf bcef ce bcf acf acef abce ae cef abef af abce acdef ace abce cf bcdg bce ace bcf cdg e bce bcef bcdef abce ace acef adf ace abf bcef ce bf bg acef be ae aef bef ace ag abd e bce cf bdg bce f g abd e g adg cef abcf bcg acef be ce abf bcef ce bf abcg bcdf g abd cg bef acf g beg e bce bg abcdf acdeg bcg bdg beg bcdf g beg acef abce f ad abef ce ag abef bcg cg deg abdf df ae bdg abcef ace bdeg b bdf abe cdg abcdf adf acf acef adf ce bcdg ab abdf df ceg bcdf df bcde abcf abcd bdf g abc bdf bce bcg cef adf ce acg cdf ae acg beg acef abce dg bdeg acdf ce ag df abdf abce abeg abdf bce adef abcdg abcef ad acg abeg abcdf bce abg bdf adf acf aeg abef ce df acdef bcdf abce f ad bd adg bcf acdf bdf fg abd bcdf bce bcg cg df f acg adg d cde deg bdf de bfg acg df ce ag bcg bdf bf deg abdef df bcg bdeg acdf bde ag adg bdf bce adeg acg acdf bcdf g cdf acd acdf abg bcdf df abcg cg cde ae ag acdf bcdf acg beg abcdf df bg abcdg cdf abcdf abdg adg bcde df deg g de abcg abcdg cde ce abdeg bg aeg adf bdf bcdef df bdf cg beg bdf ade abcg bcdf abe abceg abcdg df bdf bdg beg bcde acdf adg ceg adf abcdf aeg cdf bcde abcdg beg ad bce abcg bdeg cde abdf acg bceg bde adf bcg abde df cdg eg adf ce acg beg abde cdf dg ceg de abdf cg abcd bdf ag deg e adf dg eg df bcdf aceg df bcde acdf cdg bcde de acdef ad acde ab² df deg bcde abd bceg g bc adg abdeg ade bdf abcdg bcd abdf cdf abg acd de dg acg cdef c abc deg abcdf df acdg ad adf abfg cg deg e adf bceg bcdf df bceg bdeg acdf bdf bc abd bcde adf dg aceg be abdf bdeg cdf bdf cg deg e adf acdeg ceg bd bdf bdg acdf f cdf adg bcdf df ac abc be abdf bc bceg ae df abcd aceg adf abcg abdg abe abdf cg abceg e adf adg aceg abe abcdf ag abceg ad acg cdg ae df abg abcdg abd bcdf abdg abeg bdf cg acdg bde abcf ab² bcdg cde bdf ag bceg ace adf adeg aceg abe bcg abcdg abd acf ab cdef ae df bcdf bdeg abcf abdf aeg deg ae cdf ac bde df dg b abe bfg bcdg bceg acf acg adg ae abe abdf bdg be e aeg ac ae bef abeg cf adf abdf abc fg af acg dg ace fg abg bcdg abf bcg aeg be f g bg bdef fg ac aeg be ab² bdg abceg af adf bg ceg fg ab² aeg fg bcdf cg bceg e df abeg abc bcf abdf aeg acdeg ce bc abg af bcd abdf bc abcf bdf b abe af adf beg ceg bce ac b bcf beg eg bf acf cdf ac abc cdf abdf bcdg bf bdf df abf abcdf df bg e fg abcdf ag bf e aeg bcf abc df abg abcdeg abce bcdf acg bg ae fg bf cf abce abfg abdg bf bdf ag abg ace fg abcg acf abf abeg bdg abf ace abdeg bcg ce def acdeg aceg abce abfg aeg abcf ae cg bf af adf ab² g abe bfg ag bcf abcd fg bg f bf acdeg abc be ace bc abeg ae acdf abg af bcf bcfg bdeg bf af def beg e fg bg acf abe abcdf cg abf ace cfg bceg f bce abg eg be abdf acg abcf abd cg beg af bcf ab² eg abe ae ag beg e acg bg acf bce bfg ag be f ad beg abd adef abg cf abce bcdef ceg abe ae def abeg e adef bg acf cd cf ag bcf e cdef abeg abd abf abcdef eg d abfg g adg abd acdef beg e d bcd ceg abe af d bg e bf abeg abd abf abcd eg d ace cdef bcg ae bcf abg g bcf cf g ad abd def abceg bdg abf abeg cg abf cf d abcg acf ad bceg af abf abcd bdeg bcf abd ad bcg f bcf bd acg abcf bcd ag beg af acdef abcg ceg bf cdeg cg bf abcd bdeg abcg f def abg af abf bd aeg abcf abdef acdef bcg abcdf abcf deg e abcf bdef cg ade bd bdeg abd acf cd abfg abde bf bd acg acde cf cd ade abcdf d cdeg g adf abd def beg af d abcg acg bcf abcdef ag bcf abcd cfg de aef cd abg cg bcf f cd adf bdef bdeg bcg abcdf acd de cd bdfg af bcde abceg bd cdef acde bdeg acdef abcdef acd abf abcd aeg beg f abf ade abcdf acd bcdef bde bcg abd bcde bcg bcfg bcef bfg ceg bf af abde abcg bd adef bg cef cd abfg eg cfg af abcde abeg bcd bcf beg g d adeg bcdeg cde bcd abde acdf bd abf abg f abf af abde bdfg bcdf abdeg deg bcfg abcef ade abcdg acd abcd bde abg abd bef abceg abcde bf acde bcde fg acef bdeg bef f bf cdg bdf ad abceg abdeg acde aef aeg deg cf def abeg bde bf de bdeg cde bdf afg de bde adf bceg abde df ef eg de f abdeg bdef abde fg ac bde de f abdeg ade ef fg beg bde adf c bcde ade af abcdeg cdeg bcdf cd deg bcde acdf bcfg bdeg cdf bcdf abdeg cde ef b beg bde cdf ef bdeg cde abcdf aceg abdef ag abef bcfg bcde acdf ef aceg de aef bef cde aceg acd acdeg abcde cdeg aef abdfg abg abcdf adf cdeg bde abcf abd bcdg beg acef abdfg bg cef bc abeg cg cfg ac aceg de acf ad cdg cg abcef aef acg afg ef bdeg dg acg abc beg bde cd adfg eg acdg ef ab abcg dfg cd bceg eg abc aef bdg bcef ef b beg acg b c g cdg ef b deg bde bcef dg ag abf adg bdg abcg abcd ab abcg ab² abc beg ag abc cef abdg abg bdf abcef abg acg d cef adfg bf acef abc cdeg cf adef bceg cg abc ac bdg abcg aef aeg abg bcd b acef g abef aef aeg cde cf b adeg abcd cdef ab² ag cfg af bdg abc aef ab cdg cg bef abe cdfg bcf bd bc ade bcd b beg abcde ab c aeg afg abcd b bg abdeg bcef abceg cefg bef ef ag b bcd bc bcg bfg acd aef g abcg c cfg cd bdf abef bg g ab be ag abf acef bcdg bg aef bc deg bdeg bcf bce bdg abcg bcd ace befg abfg d cef acg bf ef cg dg acef abef bceg abdg cd acef ae fg bfg bcef abf ab² bc bcg bdg abcef aef bcdg acfg abce abc dg bfg abef abce ceg ab abce ae abdfg bd ce abcg bfg ad befg abcdg abcg aef bdg bg cef acdf abe bcfg d aef g bcef bdf ce dg bcfg abef adg bcdg ad befg ag fg bd eg cdg f ad bce abfg d aef e fg bcd abcef dg acg abef cef bcdg bf abd bdg acdg bd abef adg abdg ad acef abdg d aef bcdg cdg bcd fg bcg abcdg d aef abdg fg abd ae abg bd abef cdg bcdg cd acef ae dg abfg abef adg bcfg cd bce bdg d bcd bcdg adg abd cd acdg bcfg acd aef abdg ab acef bdg abcg bd e cdg ae ad ef bcdg d aef bcdg adg bdeg bef bce acg b abcfg abdg abe bcd abcef acdg abdg fg acef cg fg dfg bdg abcg cef cefg adg ag bef befg abcdg adg f abdg bcg cdfg acd dg acg bcef bcefg bcdg ad cf abcdg acdg af ad abfg ag def abcdef aefg dg abd abdfg deg abdef acd acef acg acd bcd bcdg ad bd bcf dg abdg bf acef abdg beg acef acfg abcg cef adef adg bcdef d acdfg abdefg adg abd cd cdg bdef d acdg acg fg abfg bdeg dg bd acd cdg bcdef cd abfg cg acdef bd efg cdg bdef ad adg bdg d abcfg abcdg adef abd abcef cdg abcd d acdg bd ad bcd ag cdef bd fg abcg cdfg def acef bcdg adef bd bdg cdg abdef afg abg bdef d adeg abdg bc abd abcdeg acdg abdef acfg bcefg abdef bf bcfg bdg def bd efg cdeg abdef ad cf abcdg abf bd bcdg adef bdef aefg adg abcdef d dg aeg abef acf bcf acdg cf fg f abdef acdef defg bdg cdef abcd efg adg abcdef cd cf bdg bcf abcfg bcdeg adg abd bcdfg beg bcdef def adeg abdg adef abcfg abcdeg cdg bd abcf cdeg c acdef abcefg bdg def abdef bf adg bdef abcef af abcdg bf abd bcdeg def abd bcf dg abdef cdef adg c cdef bfg abcdeg abc abdef bcdeg adeg bdef bcf bfg aefg cdef f bf abefg bdef abf acdfg bcdeg cdef f bcdg def cf efg cdeg bcdg cd cdeg c abcef bd efg acdg bcdf bf bc abcdef d acdeg b² bcef cdfg abdeg bc ef bcf abcg b² cdef befg c adef af abdeg b aef afg adg bdeg acdef cf bcdg cdef abdf aefg abg bdef acdef bg efg abef abfg ag beg cf bcf abc bcdef acdef bcg ag deg bfg eg adeg cef bcdeg abg abcdg df cf abdeg adef acdfg cg dg acef fg abcg

Monoid Structure