Details Page for 0.5323

Complete Solution is Known:

MSV File: q-0.5323.msv

Growth Pattern:

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Details for Q₁₇₃₂(0.5323):

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 c 1 ab² ab b c c b² ab b ac ab² bc ab b b² ac bc ab ab² ab² d bc c ac b² d ab c ab² ad b b b² ab² abc ab ab c bc abc d b b² abd bc c c ab² ab² abc ac c ad cd bc ac c acd b b abd ac c bc ab bd ac abc bc ab b² ab² abc bc bd ac b² abc bc c ab² d abc bcd b² ad abd b ab² c ac abc bd bd b² bc bc c ab² d ad abc abc b d ad bc abc c d bd abcd bcd ac ad ab b² c ac e bc ab² b² ab abc bd ab² d b bcd b² abd ab b e ac ac d b e ae acd d bc bd bd cd abc ae abd ab² d be abc bd ad ab abcd abd e ad b b² abcd ac c be ab ae e abc ad bd abd ce acd bcd bd bd e abc bcd abd ab² e de abcd abce cd ab ad bcd c be abc de bd ac bc e bcd bce abce ae abcd bcd bce ab be bc bcd ae ab ab² abcd de ac c ace abcd abcd cd ade be ab² bce cd ade abcd abe abde acd abc bcd cde ad ab² abc bd c ae be abd bcd e acd cde abd bde ac acd be abd ab cd acd bd f ad d cde ac bcde b e bd abcd bde ae abd bd be f ae b² bd af ad abc abd abcde d ad ade bcd abcde be ad ace abc acd d abe af ade abcde abcde f bd bf abe bc af abd b ab cd abcd bd abd d ab² bcd be bf d af f abf abf ab abd bd bc abc ae abd bd bc cd ac abd bd bf abcd c bce abe ab d bcd abde acd be ae c abc cd ace ce abd abf abc de af cde b e ac f af bc ab² c c df abf d ae abcd abc be e abd af bc ac e f bcf bc cd e abcde d abf ade ae b d bdf c bcd be bf bf c ce abc abf acde abd df abc bf c f ab bde bf c bd ab be abf c f d b² ce c bc abe ab² ae f acd abc bdf abd ab de c acf cf b abcde c ac ae bcf abcde abe ac cd b abcf ab² af abc bc b ab² cf abc bdf bcdf ab² df bc abce c acf b ab abf c cde b de bdf ac acd be cdf bde cf f b abf bd d af bc bdf acf b df abcf c ac d ab bdf acd cd abcde ad ab² bdf bc abc abce ab² af acd abc de abdf bd bc bc ac ef acf ab bcdf ac ae acde abef abd abdf ac e abce ab² cf cd bf abe bdf b² ae cde bc af ad b abf abcf af af b bd bcd ac abc ad bcf b² ae cd df abd d acdf bc ef abcdf acef af acdf ac bdf cf b cdf bcf abc ade acdf bef bcdf bcd ad adf abce abcdf aef abc acdf acef ace acd ab abce c bdef d acdf ae c ef ad b abde acef cef ace adef cdef abdf bc ab bef bd acf bc def abd bcdf ad abcef bcd bcd abcdf ad abcef abcf bcd bcdf ad bd bf acd ae cdf abd bd cef bc c abcf ab² cef adf cdf c abcdf bcdf adf abc abcd abdf cde cde bd abe ce ae acdf b² abcdf cd ade def c abcde acd be abde abd bcf de abcd abcd bdf abef df cdf bc af acdef d be abcd abdef cd cdf abd abd acd acd acdf abcdf bdf cde e abf abcdf d g bf abcdef abdf bdef cde cf ag abdf ae acde g aef abc bc df abd abde d bc df ab² bcde def adf bcd bde bdf acdf ae bcd abdf abf ace abd bef acd abc e ab² bce bdef bc acde abcde abcde abcef adf g abcd ad d df bd bcd bcef d cde acef abcdf def ag bd bcdef ac g acd af b² ef g c bg bg ad ade f bcd bdf b e df af abc g abd abg bde abc bcef g bd bg abc abef bcg abcdf bcde cdef ade abdef abcde abg cg ag abc abcdf acg d acdef bcd bf b abd acf bde abc bc abcg ab² ad bf abcd f abcde bg acdef cd aef acef d ad ag ef bc abcef df ab² abce bc abcf ace ab² ef abce acde cg f ab bce abf abde bcdf ad d ag bcd bcg bcde ab df ac af bf adef acde cef abde cd bef acde bg ag bf acdf bcde bg ad ag c bcg ab bcf ag abcd be adef cg b² f bg be ag abcdef af aef be ag ce abg cd g acg f ad abdg abcf abcd af b ad de c abc adef def ag acef bg bdg bef bd ae acef abde bde cf af bcde be cd cg abcg d ag e f bg ab ab² ag e abdg cg de bg abg cd abcef ace ab² abg bc cdg acg def ad bce g acf bcg d d e abcd bg cg ag ab² dg df abef acg ae bdef abg ade acg ce cef dg abf bcd acde adf bf cg cdg def bcf g abd bc cd b abcf ce ag bc bcf acg ace cef d bc acg aef bcg bdg abf cdg aef d bdg aeg bdef abcg bcdg cg ag bcef df abc abcdg b aeg df bce cg cf acf cdef abef abdef cdg abcg bcg eg bcd cde acde bce bcdf e ace cdef aef bd abdef bc bcg bcdg abcdf beg b abe bef adg af d abce bde bdef df ceg ag c c abcg d bce adg ae bdg adef cef bd bcg c ag abcde e adef cdef bf bcd adg acdf abce abd bcd cg abcg bcde adg ae deg adef abcdf bcdf dg acdf ceg abd bdf cdg acdf abcdg abdef b ace acdf abde bcdf bcdg ab bdg bcdef abcdef ace def acdef ag adg cg abceg cdeg bd abc acdf be bdeg bcdf ab b cef bdef cdg adf bdg af c bef ce d bcg abcdef bc acdef acef bcdf g cd cdf bceg bd g ae acef bde acg deg acdef abdg bdf abdef acdf abcdeg abeg abcd dg acg bd af abcdf ae bdg abcdg bde dg df bc abcdg bcde abcef afg def abcde bcdf acdg acg ac abcd dg cde acdf abeg bdf af bc ad abg beg acdeg acd abdg abde abcdef de abc abcdg abcg dg cde bcdg bde bdf aceg bcef acdef abcdf abdef ae acg bcdf beg aceg acdf fg ace abcde dg cd bdeg beg ce b g cd abceg abcf abcef deg abdg abcg abcf abcdg bdg fg ae abef g bce abg adg abdef cdf dfg acf bef c cfg bcg acdeg bcf bdg ac bcd bef acde abdg af bceg bef cg acef aef beg abef cfg acf ad bcdef bc def abcdeg bcg bf bef cdef cf abce bcf ag acdef abcd fg b acdeg cf abfg bf de cde ef bg abc abef cef ab² deg bcf abcd acdeg abcg ab g aeg acd bcg ag aceg abdg abe bcg bef bdeg ab² e abef abc acfg ab² adeg abcf abc c aef abeg bf aeg af acdg adeg cde dg c f ad bd ag cef bceg acg ab² ce bg abcf bcef acdg ab² abg cd acd cf bg abfg abef g c bdf cdf ag ce ac beg bcef b aceg acf abfg abc cdeg acfg ab² beg abc ceg cf abceg cdf bcd ac af abg bef g abcd def abcfg bce ceg deg abfg abeg abd ceg ab² bcfg abcdeg ag bdf b² abeg g aeg abcg abcdeg ab eg ace abceg beg d abcef dg abg abceg abcdg bdf bg abg bc cfg aceg acef bg bc acg cg acf beg bcef c ae bcg abcfg g abdef ace beg bef de c abg bfg bef d dg cef abfg afg afg abd bdg bdfg fg abcd abcg acdf abcef c f df abdg ag bcdf ac adef abcdg b af bg def cg abcd abdf cef acdf abc abcdef acdfg d abe fg bcdf ceg def bf bcd dg bcg acdf bdfg bdf dg fg abdeg bdfg abd aeg cd cg abef adeg adfg ad g c cdg adef bdg abf bcde afg df beg ag deg ae abefg bcdeg acf cfg ac adf bdfg bcdef aef cdf bcdeg aefg ace d de bfg abdef cde defg d bdg abcdf deg acdf d bd abcd dg def bcdg abcfg abcdef adfg cd abdef ab adeg dfg c bdef ce acdeg ad bcdfg abc cdg cdfg adef abdeg bcdef bdefg abcg abcdg abdef abg cdeg adef bce ce dg dfg g afg bcd bcfg def de abdf defg acdg d abdeg af deg abcf cefg bdeg ae deg abf ad abd bd deg cd bcg abd bd cdeg abceg bdeg cf dg abdg de abcefg bcd b ad abce abcdef adeg acg adef bdeg bd dg ceg def cg bg fg acdefg abcdeg abcg abd def ag bg bcde cdg bcf d abg abcef cdg abcdg bdg bg abcd afg acdef efg bd adg ag cd cf bd acdfg acd afg bfg ce bf d abe bcdf acdeg abcf ag acef abcd bc cdf aef bcefg abeg aeg fg ef bd cdfg g abc abcg abd acdeg ag def abdf bfg d abcf abeg bg abefg cde abcdfg af bg bf acg cg bd bcfg bcef be bdfg abcde bd abf be af acf bce ceg ag acd bdef defg b abcdeg e h efg cg ef beg abf abcdg fg abd abcfg acfg abe aef f h bdg aefg bcd abeg befg bce bdg bcd abfg abc g cdfg acef abcd cdf defg acf abg bg abce adef bd ce bf ag def f ce bef cfg acef adefg abef abcef cdef ae acdefg abef acg def f acdefg abf ceg cf bcfg bcfg h g bcg bcdef eg ag adg beg bcfg d abe f abeg abceg abef acfg acef abfg bef abcdefg abcde abd h h cdeg abce bcg abfg be fg ce bfg bcf bdg h acf bh acde cfg e abh ah abcdg abce cf dfg ade bc fg cef abcfg bcef df acf cdg bcfg bdg abcdf abcde abefg b cfg af h abdeg bcf fg acef abcfg bfg acd abcdefg acdg abeg abcdeg bcef abcde abcdf abcfg bdfg bcdefg abde acdefg abfg bdefg cfg bdf abeg cdf bcdf eg e abeg abef aceg bcde adg abeg abef acdeg acf cdef acdef be cefg acf abcfg bef acefg abcde bcg cdefg bcef eg ace dfg cdefg ch abcdf ac abeg abdeg acg bcde ae ah bcdfg abh cdg bcg df h bde ace bcfg acde acfg abdef acdg adef abce abefg bde cdefg b bcdg acefg cdfg h abc afg abcde efg bceg be fg abcde dfg cdf abcdeg abdf abcde bcg cdef bdefg abdf adfg h abef cefg bcdf adh df abef abde acdg acdfg def h deg dfg ch bdefg bcdefg h adefg acdf abcdfg abde abdef abeg cdf ach bcdef bdf h abcdg ch abdf abh abc afg bd ch acdfg ade bdfg abdh bcdf be abc abcdef bcde acdg adf bcdfg bg abdf defg d bcdeg bdf bde aef bef abcdef ch dfg ade cd bcde bcdf acde adf bdefg bdef ef cdef abcdfg ach adg cdg acde bcdeg dh ac abf def bcg abcdf cdeg h abc ace bdf acdfg acdef ah abcd abcde ch acdf f bdf adfg acde adef abcdefg abdf acdfg cdf acdf ach h acdefg df cf ch abcfg acdfg bdeg abcdfg ce abcfg adefg df bdef aef def adefg acef af abf defg acdf abcdefg ach bh acde bdefg abcdef e abh bh bdef bdef adfg cdeg cefg ace abcdf acdeg b bcdefg f bcde abcf acde bdeg h abcfg abce d bcdfg bdf adeg ah bch ab² aeg deg de acg ch abcefg cdef abf h abdef ach def bdfg bdh abfg abcde ch bdefg abcdeg adeg acdg cdg cf ae ah be abdfg ace ch abch be abh ce abcf adefg aeg h bcg abcefg bcf cfg af bfg deg def abcdeg c adg bf cg cf ch bcfg de acfg acf abcdef adh be f acf abcg abcf de abdg bcg adh abh cfg acef bg bef ade abeh abcdef abg eg abcdg cf ab² acdh adh eg bh cdh bcef cdef dh beg abcg bce afg aeh bcfg ah bcf ab cef abcfg acdeg afg bch abcdef bg eh h f beg ach bcef aeg ah bfg ad cg efg cdg befg abef bdeg bch ce abeg acd acfg bch abefg abefg abh afg acf cdfg beh acefg bh cdg bc bcef g abdf bcg bdefg bch ag abceg bcg abcf bce bch adg abf dh cg bch abg bcefg h acg abcdh ach ach fg ah ef adeg abcef aeh ae h abefg acdef g acef df ah abcdh bd beh eh dh aceg efg ce ch abe cg bcd abcg ach abdefg bcdef bh aceh bcf ceg cf af abcg abcdf acdh eh ae bcdg fg bcdf abd de bcdefg h aceh bg bdg abef adh adefg ef ch adeh beh acf bcg bcf ad cfg bcfg abcg bdfg bcde bch adfg adef bdfg cefg beg cdefg abcef ah bdef abceg bcdh abdg abdf dfg acdfg abcf aeg beh ah def afg acg abcdef cdfg abdh acde aceh abcde adefg de abdeg bcde acdg beh abcef g bdf adfg ach abdeg cdeh fg abcg bcdh bcdf aefg bh ah abcdfg bcg cdh bg cdef bdg bdfg acdg abeg cdef ah aeg cdg abefg de beh deg dfg adef d bch cdg cdefg abce bcdg ach dg ah acd afg bdef dg bceg bcdfg bdfg ce defg cde abdg ah abd acdf abcdefg abdg af adg bcg abcdg adeh abcdef adfg bdfg abcg ac defg cdfg cd adfh bcdf defg cdef abdg bdef acdefg bcde de acdef ah bdh acdfg abch abdg abcdef cdeg d bcdg ach defg defg abh bcdg ce cdefg ag abh abdfg bd acdg acdf acd dh bdef abd abcf bdg deh h bdeh bce ch eh adfg bh bcdg acf abfg acdeg acdef bcdeg bfh defg dg cdef abcdefg abceh bcdf bc ch acdeh abceh adfg abcdh bdg beh adg adf cdf cdh ch adefg bdh abef abdefg acf beh abe dh abceh bd ch be abh adh beh abcef ch ach c acdg cdeh abdg ab² abcdef adfg bef abch abdef adg df fg ace bcfg adg beh aeg deh bdef bch abe aeh ae cdg bef bdg cdh bcdef abh bcf abcdefg abcdf dg bdh def ceh ace dg bh afg aceh ach abcdh acefg ah bcdf bcfg abef efg abdefg ac ce bceh ag befg ae bh b adef bch bcdef abcef bh ef c abcfg acg dfh ef ce beh cefg aeh bdefg afh cdg abce abdefg f abeg adefg fg ach bg bh afh bcdeh ac cdh bdeh b af e abcfg adg fg adh bcdg abce abc acfg bcfh abfg bceh bcf cfg eh abg h abce ach bfg beg abh ab acdh abefg abcf abeh h ab² bcg abcef abe h acdeh bfg bch acfg abcfh abcg ah bce aceg abcdf ac abceh cefg aef ch bcef de aeg bcg befg acfh bfh abdh cdeh abeg abef aeg abdf ae abcdeh cg acg bde abg cfh ab acg acdh ac abh aeg abcdeh abcde abceg dh g ace abcg ch cg acefg cdeh bcg cd abcf abde bg abeg aceh abcdh bcde e dh acfh bcdeg ch bch def bdfg bde deg bcfg acfg abc abdh abfg befh cg abcdh dh dh d acfg abeh abcefg bcefg bef cg acef cdfg cefh acfh cg ace ch abcdfh ag ef ab² abch abdeh cefg bh bcg cdh bdeg aceg abg bg adh abcdh abdg abcd abcdfh abef afg cdh ch bdfg ade bd cdeg cdh ach abcdef h bcde bcg cdh cfh eh abcg abcfh d aefg abcd dh ad abef abcdh bcdef bdg abdfg acg bd bcg cdh cfh cefg ef bdfh ach abdefg acdefg bcde bcdfh bcdfg bdeh cdefg dfg beh bdfg bch bcdh abh abcdefg abcdg abcefh bcd abcefg bdg bh bd cdeg acdef aeh abdh bcde cdeh acd abdefg abdh dfg abceh d cg cef adh bh abcdg abcdh acdfg cdefg de bdeg ce adfg cdef ac bdeg abde deg abef abdg abh abde bcg acd abcdfg cfh cdefg bcfh cde bcdh ce acdfg ah acde adfh abcde acdfh bdg bdfg acfh bcde adef bcdfg abdfg ace adeg acdh abdg eh bh dfg bce bdefg afh acdfg adef abefh dfh abcdh dg adh d ce bch ach deh abcdg aceh cdg deg bcdfg acfh af dfg abdefh abdefg acefh cefg cdfg bcefh bcdg acdh adfg dh bce bcdeg bcdh acdfg abe ag ce aef abgh bcefh abcdeg bd dfg cfg g cef bh adg acg abcdeg adefh cf cdefg abc abdefg bcfg deg cdef bce cg ce acdeg dg ade ace adefg acdeg bcdh aceg h dg bgh bfh bcdeg adeh bdh ad adef cdh adeh acdefg abce bdfg ae bch abdeh bfh bcfh gh acefh bce ad ah ab² abcg b abdeg ah f adeg efg abcdeg e adefg ceh abefh ch cf abh abce h defh acdh abcdefh bc ceh aef adefg bch abdg abh ce cdeg ab ach bcgh abg abdh fg abcdefh dg bcfg ah bdeh acdeh abcdh aefh bc bcdg cefh deg adeh bfh dh ace bcg bcdh abcf abgh e bcefh bce bcdg b² adeg cefg aeg bcdeg c aeh abe abcdg acdefh bcg abcdh bdg abcdfh bcde bcg abdeh def efg bh bcg aefh cd abde abeg cdeg bce eg cdh adefh abcefg abce bdfh bceg bceg abgh fg agh abcg abch cd g abfg ef aefh be abdeh ah abfg abgh acg aefg dg abfg adef aeg abcdh bcfg acfh acg abceh ac abg abgh aeg h bdef bceg cfg acfg abcdefg bd bdef ab ach dg abg abceh fg acdh bcfg dgh abh fg ach bcg bcgh bcfh dh befg bceg bch abdg abh abcg acdeh cfg bcfh dh bfg abcdefh abc aceg aeh cfh cdfh ceg acfg abcfg bceg fg aeg bcdgh bcfg abcefg ag bh abfg aefh aeh bdeh abcd abefg acefh acde beh adgh abg ceh afg ch cgh abg h acg bcde acdh bcfg cefh afg bdef abfg bcfg abcdefh h beg cdeg bceg aceg bdh bh gh cde bcd bcdfh bcefg bfg efg bcdefh ach eh abcef fg abgh bfg bch cdgh aeg abcde agh acfh cfh cef gh abdef cd bdg befh dfg bceh abgh bcgh adfg abcfg h ag dfh bch acdh bdeg bh abgh cdg beh bdg bdefh abdh adgh ceh cg abdgh cdefg ah bcdg abcdh abde adg d bdeg abcdh cdfg acdeg cde bcdeg abce bcde ach bcdefh bcdefg bcdgh bcde aeh ade abcgh cef cdg abcdfg cd beh abcdef abfg begh bef deh aegh bdh ade abdefh cdh acdeg acdgh abdeg acdeh aef befg abcdfg aegh adh abfh bgh cde bcdeg abh bdh agh abcdg abgh bcgh acdeg bdgh aeg bch f eh bdfg acfh abcdh abcfg acde bdg bh cdg cdfg bcdeg bcdeg abcdeh abcg bfh acdf eg bcgh acdg adfh acdf bcdh bde bcdefh bdfg ace aegh acf eh ade abdeg abcegh defg acfg bcdfg abcdefh cdfg adefg abcdfg abdeg abceh abcde gh bdg bcdfg abeh acdg agh cdf bcdh abcd adg cdgh bdeg abcdegh abcde bcfh abdeg abh cf acdg aeh ag cfh dfg abdfh abcdfg abcdeg cfh cdefg acdefg bf e abde cdeg acg bdfg bcg abde abcfh abdfg agh begh cdg bdeh abcdeg abdg ef acdeg bce abcdfg abcdgh dfg abgh abf cde afh abg acdefh abcf abcdeg af bcgh dh cdf abdegh befg ch acdgh g abefg cef abdfh acfg cgh bde abcdefh bc bdg abcdgh bh dfg bc bcdeg cdh dg abdeh abf abdefg abch cdeg eg aceg begh acf acdeg cg cdgh ah ef acdh abf abdefh e bdegh aegh cg adeh dg dh bcefh bdeg bcdh cdfg ah bcefh ceh bcdeh defg abc bcfh acdfh ab² abce abcdeg abf abg beg bfgh abc acgh abcg abh bef cg ce abdf cd be agh abcfg abde cdgh g ce ace abcegh bcgh bcef acefh abcg degh b bcd bcdefg abg aegh aeg bdefg bcegh abh ab def abefh abg abcdgh acefg abdfg gh bceg bcdgh bcef bdfg bg abgh bcdegh abcef cgh abeg abefg acdh ag abegh bh dfg ab abdfg bdf bcefg bh acg adgh abcg acd bce bdh abgh ace abcegh bc acgh b² beg ach abcef adefh abeg acdeh bfh bcdh acdefh abg adfg g bcdef abcdf acegh bdh acefg adfgh e cefh abcdgh ah bcde bceg acegh ag cgh bcg bcg be efg adeh abcg bgh abfgh acg abch bcfg adh abce abcegh eh cdef abcgh abdfg bcdf befg abefg aeg bcef abcdef beg bcdh abf begh abcefg abg adf cg bcgh bcfg beg ab efg aefg aefh cdef afg ceh abdf bch adef abe aeg bfg bcdh cdef eg abdef abg bcdh aceg abcdegh dg h ef ab ch bg ah acdf abcd adgh bg bdg aceg bceh aceh abcfg adf adf bde adg adef def cgh fgh bceg adgh adf efg bdf bg bcdg afg bch bceg efh cdef eg cdg befg acd cfg bdgh bcdf abcfg bcdeg abdg abdh dh bcg abf ag adg adfg agh abce cefg defg abfg ad afg abcde acdfg bcgh cdfgh cf bdef cdeg bcdfg ceg h bcdef abfg abcdg acfg bcegh ab abh fg aefg deh bg cdegh acg abcfgh bcdf abcfg bh acg bcfgh adefg acdgh acdf bh adeg acfgh abch bdg aegh beg fgh abcdeg bdg bfgh cdefg abdh acdf adegh bcfg dg fgh bc abegh acdfg abdeh bcdefg abcdg abgh abdef befg bcdfg ab² adg abdfgh dfh bdg cgh abdef acdeh bdegh ach acef dg bh acd aef ch bef bdh abce abdgh adg bcfg de cfh begh deg abdeh acdef bcdgh acdeh cdg bdgh bdg beh adfg abh h bch cdh fgh bcdfgh bdg bdgh adefg acdeg abdefh bcdg bdgh dg abcef abcdeg bdg cefg cf begh abdg beh dfg abdef abcfgh abcdg acdh be adg cfh bcdefg acdh cdefg acdfgh bdh bdfg cefgh dg abcdgh cdef acef acdg adefg abe abcdefg ae bcde bdfh abcdfg abcdeg fgh acdeg aceh cd c cdeg abcfh aeg abdefg befg abdf cdgh bdfg bdeg bgh defg acefgh bdfg bdh acf acg acdefgh bcdfg ae af ceh abdfg bch acf cdefg adh bf acefh cdeg cdefg abcf bdfg ach acdh acgh bcdfg acfh cf defg bdfgh defh cef adfg cdefg adfh abf e bcefg

Monoid Structure