Details Page for 0.1732

Complete Solution is Known:

MSV File: q-0.1732.msv

Growth Pattern:

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Details for Q₃₃₇₀(0.1732):

Q = <a,b,c,d,e,f,g,h | a²=1, b³=b, b²c=c, c²=b², b²d=d, d²=b², b²e=e, e²=b², b²f=f, f²=b², b²g=g, g²=b², b²h=h, h²=b²>

P = {a, b²}

Phi = 1 a a b b ab c b² ab² ab² b b ab c ab² ab² bc b b c ab² ab² bc ab ab b ab² ab² bc bc ab c b b² ab² bc abc ab c c ab² b² b abc c c ac ab² ab² abc ab c c ab² abc bc ab ac c ab² abc bc bc ab b c d bc bc bd c b d d bc abc c c ac d bc abc abc c c ac d bc abc bd b c d abc bc ab² ac c c abc bc ab² bd c b ab bc b² ab² ab² b ab d bc ab² bd c ab d d ab² ab² bd c ab d bc ab² ab² c ab b b ab² ab² b² c ab b d ab² ab² c bd ab d bcd ab² bd b ab d c ab² ab² bd b ab d ab² ab² abd abd ab ad ab² ab² abd bd ab e b ab² ab² bc bd ab bcd c b² ab² bc abc ab c d ab² ab² b ab c c ab² ab² bc ab ab c ab² ab² bc bc ab c c ab² bc bc bd c c d abcd bc abc bd c ac d bc abc abc c c ab² ad bc abc abd c c ab² abc bc bd ac c d abc bc bd bd c c d abc bc ab² bd c bcd d abc abc ab² c c ad d bc ab² bd c ab d d abc bd bd ab ab d ab² ab² bd c c b bc ae ab² abd c ad ad e bd bd c be d ad ab² bd bd ab be d ab² abc abd bd be d d bcd bd bd cd c b bcd e abd bd be ad d abcd e abd cd acd ad d abcd ab² bd acd ce c bcd e bd cd ab c c abc bc bc cd c c bcd bc bc cd c c ab² bcd bc bd bd c bcd d bc cd abc c c ac abcd bc abc ab c c ab² abc bc ab ac ae bcd abc abc cd bd ac bcd d bc abc bd abd ac d ad abc cd abd ae ac bcd ad bc ab² abd c be ab bc ae ab² bd abe ab abc bc e bd c be d bc e ab² bd be be d ae bd c abd be d ad e bd abd be be d e e bd bd be d d ace bd bd be ad d e e bd bd cd ad d bcd abd abd cd be ad d e abce bd be be ad bcd bd acd cd be ad bcd e de bd cd ace d bcd e abd cd cd ad ab² bcd bce bd cd abe bcd bcd bce cd bd acd bcd bcd abcd bce cd ab ce ace ad abcd abce cd acd ace bcd bcd ae cd cd ace abcd d bce ae bd cd ac bcd d abc cd bd ace ace d bce abc cd acd c bcd ad bce abc abd abd be bcd abc abc cd ab² abe be ad de ae abd bd abe be d ae cd bd abe be d ad ae bd bd abd be d ad e c ace be d d ae abd bd be ad d d e ab² bd be ad d e c bd bd be d d e bd abd cd bc ad e bd ab² cd be ad e bcd c bd bc ce ad bcd e abd cd be ce d c abd cd cd be ad bcd e abd bd acd ace bcd bcd abce cd cd ce bcd bcd abce bce bd be ce bcd bcd bce acd bc ce ab² bcd e bce abc ce abe ab² bce bce cd abc ce bcd bcd bce abce cd acd be bcd abcd e bce abd ce be abcd ad e acd abd ce abcd ad ad ae acd abd abe d ad e bde bd be bcd d abce ae bd abd abe d ad e ae bd abe be d ad bce abd bd be abe d e e c bd be ad d e e bd bd be d d e bd abd abe d d e bd bd be be d e c c abd bc d ad ac e bd be abc ad bcde bcd bde abd bc abe d ac ac abd abe abe ad d ac abd abd abe be ad abcd e abd cd abc ad bcd ac bce acd bc ce ad bcd e bce abd ce abe ab² abcd ac abce abc be bcd bcd e bce ab bc be bcd abcd b cd acd ce ce abcd bce e f acd abe abe de bce f acde ab² abe d de abce bd bde ce abe d bce abce bde abd abe abcde ad ae ae abd ce ace ad ad ae abd abd abc abe d e e abd bde be ade d ac abd bd be be d c e abd abd bc ade ab ac bd abd abc abe ad ad c abd abde be ad d e abd bde abc abe d abcde ae bde f bc abe bcde d ae abd bd abe bcde ae ae abd cde bc d ce c ae bd bde ce abcde ad f ae abd be abe ad ac f abce cde abf abe bcde abcd bce bde cd abe ace bcde ade abce bde acd abe de abcd bce bce bde acd ce abcde abcd bce bce acd ce ce abcd bce cde bde ce f de de abf bde abde abe ace abcde acf bde abc abde ace ab² ade f bde bde abf de ad ade f abd cde ace ade ad cf bce abd abcf bf ade de d cde bde ace ade ad df abde abd bdf bf de ad f bde abd cf acf bcde ad f abd bd abc de ade df bde abd ace cf d d abcf bde ab² bdf cf d bcf bde bde ab² bf de abcde af af ab² bc ade ad c adf abd cde abe ad bcde f df bde bdf bdf d abcde f abde cde bdf acf ab abcd bcf ab² cde acf bcde bcde bcd acdf cde cd acf bcde abcd abcf abce cde acd bcde de abcd acde cde bdf acdf bcde bcde abcf bce bde acd abcde bcde f adf abce bdf abf bcde ac bcd cde cde abf bdf de de df bcf abc abf cf abcde f abcf acde abf bdf bcde de df abcdf abde bdf abf de de f abde bde abdf abf c df bcf abde bde cf ade de bcdf abde abd bdf acf de df bcf bde bdf acf ef bcdf bcf abde abd bd acdf de bcdf f bde cdf abdf de ad f bde bde cde bdf de abcde df abde bd bf ade de df df bde cdf cdf ade de bcf ef bde cde bef abcde bcde bcdf bde abce bef ade bcde bcf abcdf bde acf abdf ade bcde bcf af abde cd acf bcde abcd bcdf cde cde cdf bcde bcde bcd ef cde acd acf abcde bcde abcf cde cde acf bcde bcde abcd af cde acd acf bcde bcde bcf cde cde acf abcde bcde abcd adf cde bde bdf bcde ce df acde cde acd abcde de ef abe aef bde acf abef ade bcf af cde bde abf bcde ade abe bcef bde bde abd de de f bde abde acf acf abcde bcf abef ef abde abd ade de bcf bde bd bf aef de abcf bcef bde abc abd bce d abcdf abcef bde bf acef de de d ce bde bf ade de bcf abde bde bdf cef ade abef df bde bde cde ade de bcde abde acde bde abd ade bef bcd abcdf bde cf de bef bcde df cde e acd ade abcde df abcd acde cde bef ade ade df ef cde acd abf abcde bcde bd bde bce cd bcde ace abcd df cde bce acf bcde bcf bcd cde abce cd bcde ace bcf adef be acde abf bcde ce bcd be cde acd ae abcde ce abe cde acde ae e bcde abcf be bde abf e bcde bcdf be be acde ae ae bcde f be acde bde e abcde ade be be bde ae e de be be abef bde e ade ef ad ace ce ae e de be be abcef bde ae bdef de be abcf bde e abdef de de abcf abcef bde bd bdef de bcdf ace ace ae bdf bce de d abcd bde e acd de d bcd ace bdef bce bce abef ace bcdf acde acde abce bce abcde df ace ef bce bce bef ce ace ef cde acd abce abcef ce ace acde bce bce abcde bcde ace ef cf acd e abef ce abe ef bce cd abef ace bcd ef acef bce bce bcde ace abe bcdef bdef cd bce bcdf ce abe ef acd e abcde ce bcd bcdef bcef ae e abcde f be aef bce e e f d be bcef abf e abef f bcd be bf e e f bcd be bcef e e g df be abe abcef abd e acef ad be bcef bdf e e bcf ad be bcef abd ae cef d abc g bdf bd e cef ad be ef abd e bce abe d def bcef bd e bce bc abe abf abd bce bce abcf d ce g acf ae abdef abcf abe bcef g acd bce bef ce abe ace ae e abce bcdf ad ace aef bce ae bef af abe ace abf cd bce abcdf ce be acdf acdf e bef f bcd ef acdf bce bce bef ace ce def abf e bce acdef bcd be g acd abce bef ace ce aef bf acd cdef acef bcd be abdef acd ae g bcdf d abe bf bce abce f adf be abe acd e e abcdef be be abf bdf e abdef abcf be aef cf acd e bcf bcd be abcef abd e e cef ad be bdf e e f abe be bcef abf abd e bcf bcd be bcef abd e cef bc be abe bcef e ae bc abc be ce abdef e bce abc d abe bdf bd e bcf ad abe g bd ae df d abe bcef g bd bce bce d abe ce bd ae e d ad be ce bd acd bce d abcd ce acf cd e abce def be ce acdf cd bce bcf abcd ce g acd e bce bcf bcd ce g acd abce adf bcd abe aef ab bce abce g abcd be acg cd ae g bcd ce ab cd bce bce adf bcd abe b cd ae ab² abcd ce acdf bf cd ab² acg bcd be g b abd e acg ef be g bef ae e af be be bdf ae ae bcdf abcdef be abcef abf bd e g d be acdf cdef ab² abg bcd be bf cdf e e bcdf d be g bd e acg acg ad abe abd e e f be be abdf bd ae bce d abe ac bdf e abc ad bcf be c bd e bce bcdef abe be ce bd e bce adf abe c bcde cd abc abc bcd c b g acd bce d bcd c bdf g bce bce abcdf bcd ce bd cd abc ab² bcd ce ce g bce bce abcd ace b abdf cd bce abef abcd c b acd acd bce adef bcd ac b cd abc b² bcd c abe abcg bce ae g ace c b acdef bce bce bg ce adg acd bce e ae def ace de acdef abce ab² acg g abe abcg acd acg ab² ef be ab dg bef ab² acg bcdg be g cdef e e acg be abe abcde abd ae bcdf bcdef be be cdf abd e bcdf be be abcde adg e ae ef be be bcde e ab² bc be be abcde g acg abg cde abe be bcde e e cde abe be ce bcde ae ab² cde abe ace bcde acef abdef bce adf g ce bcde ae bce bce acg ace c abdf abce bce cde adef ce ade cef bce abc bcef c ace ade bce bce abde bcef g ab cef acg bce bcdef ce ace ade acef acdg acde adef adef bcde cef abdef ab² abde def ace b g abg b² bg abcdef bcde ade acdef e bde g bcdef de bce ab² cde dg g abe de abef bg bde ef abe abe cdef acdef ae e abcdf g abe cdef e bde ef ef be abcg bdef abg e abcdef be de cef e bde ef g g ade bef e bde ef abf ade bdg acdef acg cde ef bf c bef acg abde ef be de bcde e abg acde bcef bf abcde bcde f ab² cde adg acg bcde abdg af cde g bcg ag abcde acdg abg cde df bcg bcde acdef bdef bc acde eg bcde bcde abdef acg abce bcef adef ce g cef cde adf def g bcde abdef acg cde ef cf bcde bdf bef adf bg adg abcdg b cef eg cde def adef bcde acef cef acg bde g eg bcde acef abdg cde aeg g beg bdg abdef acg bde bcef bcef abceg f acef bg abde bcdg bcdg ade acef eg cde aceg abcdef g de acef acdg abeg e bceg bcg abe cdg aceg bde cf acf b abef acg bg cf g g abceg ceg acdg e abcdg g acd bdg bg bde abcdef abf abcg deg deg acdg bc bcef abcdg ab acdf acdg bde abcdef g bceg ac acdef aceg ab² ef deg aeg abef f beg abdeg df abf bcde bdf aceg beg dg g abceg cdef abef abeg ef bcef bcg ade ac abdef abcdef cde def eg ac abdf acg cde bdeg adef g abef bdef aceg df def abf c g f acdeg adef bf eg bcde abdf acg acde bcef abf bcde g abdef abcf def def abcg bcde abdef acg acde bcef g bcde acef acg cdg fg dg c bcde acef acg cde bf abcdeg abcdg ade abceg acg b² ef bcdg abceg ade acg acdg abde g cf ab be acdg adef ef abcg abcdg bef cdg bdeg ab² bcdef abcdg de acg bdeg aceg ab² abcdf acef b abe acdg abdeg acf abcdg abcdg b acdef acdg b² ag abceg abef abdef bdeg f beg adg adeg b cdeg abg bcef bcdef dg b abef bdg ab² ae abcdg abceg bef af bdg abd fg g b ac ace abeg abc adef aeg adeg abcd acg beg acd bcg bf c ce acdeg fg bce abcdg eg abcd fg beg abc adg eg bcde abcd abdeg acdeg cd bcg eg bcd ad beg acd g abcg c cef acg ab² bcef abcg ac c bdg acg abc abd bcg bcd abcd abe beg bcef adf bf ac ad cdg abcf cd bcdg eg f acg beg bcef bcg e ac b abg ab² aceg e aeg b bdg acg bcdeg fg abcg acf cef acg aceg abd cd ag d ad cdf adef abd afg acef acef bcd beg bd acd eg b bdg abfg bcef acd ae abceg ab abg cdeg abd acd fg cef d abg cdg def dg abceg ad abcd acdg bcef aef bcg cef bcd cdg acdg abc abcdeg abcdg bfg abfg acg bde adeg abd deg cef abfg afg bc bcdeg bce b d ce fg bc dg abcdeg b ac acg beg g bcg adf bef fg acg aef cd adf eg abdef bcd beg aef g bfg cef ce acg aceg bd g eg c bg ef abc bcg abceg abcd bcd abg bdf cd ae bfg abcd bg abdeg afg adef bfg eg bdg abg beg acd dg bcg abcdf cdg acdg bcef acd dg bcdf cef bdg acg abcef abcdg deg bdef fg cdg beg bfg bcdg bcdf cef abdg acdeg abfg abcef eg bcdf bdg acdeg beg abcef ag bcdf b bg beg bcf bfg fg aeg dfg ad beg def g abcdg bdef cdeg acg adef abdfg g acfg bfg bfg beg f bdfg bce abdef adfg acg def ef bcdg abcdg d bf beg f abcdeg bdfg bf dfg cdg beg abd g abdfg acef cdg bfg abdf ef adg acdfg abceg cdg cdeg abdf g cdfg adf cdf acg fg af abc acd bf abg abdeg bcdg ef cd adf abef abdg abdf aef g adf abf acf acdg bcdef adeg cd acdef adfg cf abcdef efg g dg eg afg ce bcef efg g abcfg bcd abg cdg ef bcf adf eg acf cf ef f g dg abef cf abdf cdf bcf adf bd cdef cf bcdfg cdeg ab² bcdg bef acf bg abeg acdfg abcf bd afg bg cdeg efg bcf ag cfg cf bg adef adf abcf abd acef ade acdeg acdeg bcf dg adeg cf cf ad abcfg ab² adeg acef acf acdeg abfg acdfg abde eg cfg cg acdeg bcef efg ae bef ad bf abcef abd bcdg afg acdfg abf bf bfg bd ae acfg acef abg ace bfg efg adg cef cdfg be def abcde f acde eg abf bcef abcde cdfg abc cde acg bdeg abcde aefg afg bce cde befg ace bcde efg ae acd befg ce bcd abdf adeg bce abef abef abcde ef f g cde df abf acdg ef afg e adf abf abg abcde efg g cdfg adeg acf ce bcdef afg bcf abef befg ce bcdfg efg bce bcf bcdeg abcd be abdeg efg abcf e abfg cf be ef f bcf abd acef cf beg efg bcf abcdeg cefg cf bdg de bcf e befg acf cf abdeg bcefg bcf ae bdef cf cg be abcf e ab² adeg cf be abcde abcf bcdeg abde acf acf acdg abcef bcf e abcdeg befg abe abcef bcf adg cef cf acdg abe aefg e bd bef cf be def bfg af acfg befg be acdf bfg abcf f fg befg bf bcfg aefg af bce acde acf bf abcd cdfg abd abce acde acdf bcef abcde abcdf bd acd cf bcef bcd abcde bdefg bce deg bf adfg abdeg f af cd cdf abf ce aefg f abcdeg bcfg bf cdg ef acfg acd abef abcfg abfg ce bcdef f bcdeg cdef abf acf acf f f bce bcfg cf bcd aef bcf abc acd abf abg bcd efg b bce abd b² bdg ef b ag bef ab² cf defg bcefg abcf abcf abc ab² acf bcef ab bfg bcf cefg cf cf bcefg abcefg bd ae afg cf be cdeg abcf e bde abcd be abe bcf abfg e cefg acf ad aef bcf ae bdef cf cf be bcef abcf e bef cf acdg acdeg bcf abcf e afg cf bcefg bfg bcf e ab² abcdfg defg bcefg aefg e abc cf abe be abcd bcf e deg afg d abf abfg bcf adeg cde cf defg bcef ac f abdefg acf bf ce aefg bcf af bdefg defg abf abcd bcdf f cd adeg bf bdeg bfg f af acef bcfg bf abdeg bcdefg af bdefg abef bf bg ef f cd cdefg abf abf bdeg abcdf f f abc ab² acg abcd cfg abcefg cdefg cefg abf efg abcdf ab abcefg abc ab² cefg acdg abcdf abcf acd adeg b² bdeg cdeg b cdefg cdefg bdf acefg cdeg adefg abcf bcf cdf afg cf defg f abcf bdefg abdefg acf cdeg defg bcf df cefg afg cf be h bcf e bdefg cf adefg abdeg ab bcf ae afg cf be ac bcf abcdeg abcfg abc afg adefg abcf bcefg abdefg abdefg cf abf bdeg abcf abcdeg deg abdf defg abeg adf bcf eg ab² bdf b df df abdefg cefg abdf acf cdfg adf bdefg deg bdf h abcdfg abdeg bh f cd bce aceg cdeg abcef bdefg f abdf acdefg bf bdeg acdfg f acdefg bdf abf abf acdfg c bdefg acd cdf bf abdeg bcdefg af af acd abf bf abdeg abcdf acfg adeg acdf bf cdeg abcdf af acdefg cdefg bf bh bcdefg abcdf af bc bdf abf h abcdef af bh deg bf abeg acdfg ce bdfg abcefg cdf abf acefg bcdef bcdf bh bcdeg acdf abeg ceg abcdf abcf abcdg acdf bf abcdefg bdeg acfg ch cdefg cdf afg abdg h d abcf abcdeg bch ab² ceg bcdf bcf acdef ae abdf ceg bcdf df ab acdefg acdf bcdefg h be abcf bh abdefg acde aceg adefg df bcf bcdeg abdefg cf abeg be df bcf e cf cf adefg df bcf g e cf defg adefg b bceg bh cf acef ab df abcf bh bcdeg abdf bcefg cdeg b bcf bcdeg abc bc bf abcdf df eg cefg bdf ah bfg df c bcdeg abdf h cg cdeg cdfg bdefg abcdfg abdf cdf acdg adf af aeg bdf cdf abf acdfg ace abcdf abcdeg abcdfg cdf acdeg bch df h abdefg bce bf acdeg abcdf f acdefg bdf abce abeg bcdefg ace adeg adeg cdf cdf abeg abcdf f bdfg ach ab² abeg cdeg f df adeg acdf cdf bdeg abcdef abcdf b cdefg abf bh ceg ace abceg abceg bcg abc bh bcdefg f ach abcdeg cdf acg beg abcdf abe befg cdef bdf aceg bcdefg bcdf d bh cdf bdf bdeg f abcdf bceg abcdg e abcdef cfg abfg adf bceg e cde h abcdefg df ach adg bdf bdf cdeg bg abe abcde bh ab² abcdfg h adf bcde abcdeg bdf bdf h adf ab bh abcdg abc ah defg bcf abcf cefg bh cf ah h c ac bcdeg bdf acde abcefg df df ac adh abde abd defg df bcde bh bdf abdf cd adf df abdefg cefg bce cdf bcefg abch c abdef abdf abce abch bd df bcde bh bdf cdf abfg h abcdf aeg bh abdf adef abfg ce bcdf bh abdf cde bg bch abcde aeg ch acdf cdf abch abch abcdf befg ch cdf bh abd bcde ch bcd acdf acdf bch bcdf bcdf adeg bh ab² ceg aceg bcdf adh bh bf cde ceg c abcde aeg bcfg bf adh acd ah abcdf d acdf acde acdeg abcdf af eg abceg bf acde ah ah abcdf abcdeg bh b² dh acd bcdf de bh g ab² abdeg acd df ade abceg aefg h acd de df abceg bcd acde cdeg cd df cdefg bh cdf bdf ceg h df bceg ae ab² cde h df abcde cefg bdefg abc acde h bcf bh bcg cf aefg bg bcf bh bh bdf bdf bcefg beg ab bcde fg cf cde ah df abch abh bh acf cde abd adf adf aef bdef bdf cde bd adf eg cefg acf acdf bg adf bcdf adeg d abdf abeg bch df aeg bh ach ab² abch abd abdh de bh cdf cdeg abfg adf bcdf aeg bc beg abde bch bcde ade ch bdf cdf adh abcdf bcdf ch abcg acdf cde abd f abdh ad acdf acdf 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cefg ade bdf cdef h bcf abch de aef ch cde abcefg abd cefg bcde acf abcefg abcefg bd acefg bcde abcd abcefg ah acde abd acefg de dg bcdh cdef adh cdh bcdef d ad defg abd f abch bcdef abcd ach abde dh abcdeg de abcdef cdeg bcfg bdef abd cfg de ch ch dh abd bch acdh abefg bf cdf bdef deh eh bcdef d abcd abcdh bde bcdf cdh bdh bf cdf acdef abde cd ch ad abe adh bdef abd eh def bf abcd aefg af acd cdefg de ad adh bdef abd bdh bdh ade abcde eh abde bd abdh ade acdf efg dh abde abdh abfg def bcd abcdefg bdef abde bce befg g adh abdfg abdef bdh adef abf adeh ceh acde abdeh bdh cdh cdh acf bcdh acdef bcf acdefg bcdef cf ceh acde acd bcf abfg ade bdeg abcdefg acdef cd eh cfg de cf bcdh bde acdefg cdh bcde abcdef d cdef abd bh acefg bcd abdf ah acdef bceh bh bcde bcdef abcdh cdef bcf eh bdefg bcdef g bcdh cdef cd cdh cdh ce ach cdef acdef bh cefg abcde bdh bcdh acdef dh bdefg acefg bcdef h abcdh acdef acdeh eh ch h ah cdef bh acdh acefg bcdef abf bcefg bh af cefg bcdef def beh abcdh cdef abd 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abcef abc abceh bcdefg abef ceh efgh cdefg abg abcdegh ceg acfh eg abcdfh acg bg abc abcdefg cfh efgh acdefg bcfh bcfh d acfh abcde bfgh abdefg bcfh ab² afgh bcg cdfgh abeh acd aceg ab² abcd cfh b acd bcfh bcdegh abcd acdeg abcdh bfgh af befgh aceg fgh aefgh acdegh bcfh bcfh acdfh abf g acfh bfgh cd cg bcdegh fgh bcdefh beh abdfg bdefgh bdefgh afgh defg cdeg bcefgh abdefg aegh ceg abeg bf cdef aeg abg bg abeg abcdefh adefh acefg bdefg fh abcdegh abcfgh bcefgh abegh bfgh f cefgh beg abf abcg bfgh eg afh abeg abcefg acegh defh f bdefg aegh abcefg defg g abdef cdefg bcdeh bdefh adegh abef acf abcde bdefg befgh bcefg abcdefg bcdef bcde abd bdfgh fh abceh abcdefg cef g cfgh abfgh abg efg abcdefg abfh ceh abcdeh bcegh beg acdfh ah abcg abcdh bcf abceh ab² bcdefg defh aeg befg fh beg aceg cf eg acdefg bcdfh cde dfgh abcdefg ag abefg cdefg cdefg abcfh bcfgh bcfgh abcdefh abceg bceg acdefgh cdfh bcdefg ah abcdfh

Monoid Structure