GroupTheory/Steinberg3D4 - Maple Help

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GroupTheory

 Steinberg3D4

 Calling Sequence Steinberg3D4( q )

Parameters

 q - : algebraic : an algebraic expression, taken to be a prime power

Description

 • The Steinberg group ${}^{3}\mathrm{D}_{4}\left(q\right)$ , for a prime power $q$, is a simple group of Lie type.
 • The Steinberg3D4( q ) command returns a symbolic group representing the Steinberg group ${}^{3}\mathrm{D}_{4}\left(q\right)$ .

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{Steinberg3D4}\left(2\right)$
 ${G}{≔}⟨\left({1}{,}{2}\right)\left({3}{,}{5}\right)\left({4}{,}{7}\right)\left({6}{,}{10}\right)\left({8}{,}{13}\right)\left({9}{,}{15}\right)\left({11}{,}{18}\right)\left({12}{,}{20}\right)\left({14}{,}{23}\right)\left({16}{,}{26}\right)\left({17}{,}{28}\right)\left({19}{,}{31}\right)\left({21}{,}{34}\right)\left({22}{,}{35}\right)\left({24}{,}{38}\right)\left({25}{,}{33}\right)\left({27}{,}{42}\right)\left({29}{,}{45}\right)\left({30}{,}{47}\right)\left({32}{,}{50}\right)\left({36}{,}{55}\right)\left({37}{,}{57}\right)\left({39}{,}{60}\right)\left({40}{,}{62}\right)\left({41}{,}{64}\right)\left({43}{,}{67}\right)\left({44}{,}{54}\right)\left({46}{,}{71}\right)\left({48}{,}{74}\right)\left({51}{,}{78}\right)\left({52}{,}{80}\right)\left({53}{,}{82}\right)\left({56}{,}{86}\right)\left({58}{,}{89}\right)\left({59}{,}{91}\right)\left({61}{,}{94}\right)\left({63}{,}{96}\right)\left({65}{,}{99}\right)\left({66}{,}{98}\right)\left({68}{,}{103}\right)\left({69}{,}{104}\right)\left({70}{,}{106}\right)\left({72}{,}{109}\right)\left({73}{,}{111}\right)\left({75}{,}{114}\right)\left({76}{,}{116}\right)\left({77}{,}{118}\right)\left({79}{,}{121}\right)\left({81}{,}{124}\right)\left({83}{,}{127}\right)\left({84}{,}{129}\right)\left({85}{,}{131}\right)\left({88}{,}{135}\right)\left({90}{,}{138}\right)\left({92}{,}{141}\right)\left({93}{,}{143}\right)\left({95}{,}{146}\right)\left({97}{,}{148}\right)\left({100}{,}{152}\right)\left({101}{,}{154}\right)\left({102}{,}{156}\right)\left({105}{,}{159}\right)\left({107}{,}{162}\right)\left({108}{,}{164}\right)\left({110}{,}{165}\right)\left({112}{,}{167}\right)\left({113}{,}{169}\right)\left({115}{,}{171}\right)\left({117}{,}{174}\right)\left({119}{,}{177}\right)\left({120}{,}{179}\right)\left({122}{,}{182}\right)\left({123}{,}{183}\right)\left({125}{,}{186}\right)\left({126}{,}{188}\right)\left({128}{,}{190}\right)\left({130}{,}{193}\right)\left({132}{,}{196}\right)\left({133}{,}{198}\right)\left({134}{,}{200}\right)\left({136}{,}{203}\right)\left({137}{,}{205}\right)\left({139}{,}{207}\right)\left({140}{,}{209}\right)\left({142}{,}{212}\right)\left({144}{,}{215}\right)\left({145}{,}{217}\right)\left({147}{,}{220}\right)\left({149}{,}{222}\right)\left({150}{,}{224}\right)\left({151}{,}{226}\right)\left({153}{,}{229}\right)\left({155}{,}{232}\right)\left({157}{,}{235}\right)\left({158}{,}{236}\right)\left({160}{,}{239}\right)\left({161}{,}{241}\right)\left({163}{,}{244}\right)\left({166}{,}{247}\right)\left({168}{,}{250}\right)\left({170}{,}{253}\right)\left({172}{,}{255}\right)\left({173}{,}{257}\right)\left({175}{,}{260}\right)\left({176}{,}{262}\right)\left({178}{,}{265}\right)\left({181}{,}{269}\right)\left({184}{,}{273}\right)\left({185}{,}{275}\right)\left({187}{,}{277}\right)\left({191}{,}{281}\right)\left({192}{,}{283}\right)\left({195}{,}{242}\right)\left({197}{,}{288}\right)\left({199}{,}{290}\right)\left({201}{,}{293}\right)\left({202}{,}{295}\right)\left({204}{,}{297}\right)\left({206}{,}{300}\right)\left({208}{,}{303}\right)\left({210}{,}{305}\right)\left({211}{,}{307}\right)\left({213}{,}{310}\right)\left({214}{,}{311}\right)\left({216}{,}{274}\right)\left({218}{,}{316}\right)\left({219}{,}{318}\right)\left({221}{,}{321}\right)\left({223}{,}{285}\right)\left({225}{,}{325}\right)\left({227}{,}{328}\right)\left({228}{,}{330}\right)\left({230}{,}{280}\right)\left({231}{,}{334}\right)\left({233}{,}{336}\right)\left({234}{,}{338}\right)\left({237}{,}{339}\right)\left({238}{,}{341}\right)\left({240}{,}{344}\right)\left({243}{,}{346}\right)\left({245}{,}{349}\right)\left({246}{,}{351}\right)\left({248}{,}{354}\right)\left({249}{,}{356}\right)\left({251}{,}{359}\right)\left({252}{,}{361}\right)\left({254}{,}{364}\right)\left({256}{,}{367}\right)\left({258}{,}{263}\right)\left({259}{,}{371}\right)\left({261}{,}{373}\right)\left({264}{,}{376}\right)\left({266}{,}{317}\right)\left({267}{,}{379}\right)\left({268}{,}{375}\right)\left({270}{,}{383}\right)\left({271}{,}{385}\right)\left({272}{,}{387}\right)\left({276}{,}{391}\right)\left({278}{,}{358}\right)\left({279}{,}{393}\right)\left({282}{,}{397}\right)\left({284}{,}{399}\right)\left({286}{,}{401}\right)\left({287}{,}{403}\right)\left({289}{,}{406}\right)\left({291}{,}{408}\right)\left({292}{,}{410}\right)\left({294}{,}{413}\right)\left({296}{,}{416}\right)\left({298}{,}{419}\right)\left({299}{,}{421}\right)\left({301}{,}{340}\right)\left({304}{,}{426}\right)\left({306}{,}{429}\right)\left({308}{,}{312}\right)\left({309}{,}{432}\right)\left({313}{,}{436}\right)\left({314}{,}{437}\right)\left({315}{,}{439}\right)\left({319}{,}{444}\right)\left({320}{,}{446}\right)\left({322}{,}{448}\right)\left({324}{,}{450}\right)\left({326}{,}{402}\right)\left({327}{,}{452}\right)\left({329}{,}{455}\right)\left({331}{,}{457}\right)\left({335}{,}{462}\right)\left({337}{,}{463}\right)\left({342}{,}{465}\right)\left({343}{,}{467}\right)\left({345}{,}{380}\right)\left({347}{,}{352}\right)\left({348}{,}{471}\right)\left({350}{,}{474}\right)\left({353}{,}{476}\right)\left({355}{,}{478}\right)\left({357}{,}{480}\right)\left({360}{,}{422}\right)\left({362}{,}{386}\right)\left({363}{,}{484}\right)\left({365}{,}{425}\right)\left({366}{,}{423}\right)\left({368}{,}{487}\right)\left({369}{,}{488}\right)\left({372}{,}{491}\right)\left({374}{,}{492}\right)\left({377}{,}{495}\right)\left({378}{,}{496}\right)\left({381}{,}{497}\right)\left({382}{,}{499}\right)\left({384}{,}{502}\right)\left({388}{,}{506}\right)\left({389}{,}{508}\right)\left({390}{,}{510}\right)\left({392}{,}{513}\right)\left({394}{,}{516}\right)\left({395}{,}{459}\right)\left({398}{,}{518}\right)\left({400}{,}{521}\right)\left({404}{,}{524}\right)\left({405}{,}{525}\right)\left({407}{,}{515}\right)\left({409}{,}{529}\right)\left({411}{,}{532}\right)\left({412}{,}{534}\right)\left({414}{,}{536}\right)\left({415}{,}{537}\right)\left({417}{,}{540}\right)\left({418}{,}{539}\right)\left({420}{,}{544}\right)\left({424}{,}{546}\right)\left({427}{,}{549}\right)\left({428}{,}{551}\right)\left({430}{,}{553}\right)\left({431}{,}{550}\right)\left({433}{,}{557}\right)\left({434}{,}{559}\right)\left({435}{,}{561}\right)\left({438}{,}{565}\right)\left({440}{,}{568}\right)\left({441}{,}{569}\right)\left({442}{,}{571}\right)\left({443}{,}{573}\right)\left({445}{,}{576}\right)\left({447}{,}{578}\right)\left({449}{,}{579}\right)\left({451}{,}{581}\right)\left({453}{,}{584}\right)\left({454}{,}{586}\right)\left({456}{,}{589}\right)\left({458}{,}{591}\right)\left({460}{,}{594}\right)\left({461}{,}{545}\right)\left({464}{,}{596}\right)\left({468}{,}{585}\right)\left({469}{,}{483}\right)\left({470}{,}{601}\right)\left({472}{,}{602}\right)\left({473}{,}{604}\right)\left({475}{,}{606}\right)\left({477}{,}{608}\right)\left({479}{,}{609}\right)\left({481}{,}{612}\right)\left({482}{,}{614}\right)\left({486}{,}{616}\right)\left({489}{,}{595}\right)\left({490}{,}{619}\right)\left({493}{,}{621}\right)\left({494}{,}{519}\right)\left({498}{,}{625}\right)\left({500}{,}{620}\right)\left({501}{,}{628}\right)\left({504}{,}{629}\right)\left({505}{,}{631}\right)\left({507}{,}{632}\right)\left({509}{,}{634}\right)\left({511}{,}{600}\right)\left({512}{,}{638}\right)\left({514}{,}{641}\right)\left({517}{,}{535}\right)\left({520}{,}{592}\right)\left({522}{,}{647}\right)\left({523}{,}{640}\right)\left({526}{,}{651}\right)\left({527}{,}{563}\right)\left({528}{,}{654}\right)\left({530}{,}{657}\right)\left({531}{,}{603}\right)\left({533}{,}{643}\right)\left({538}{,}{661}\right)\left({541}{,}{659}\right)\left({542}{,}{653}\right)\left({547}{,}{574}\right)\left({548}{,}{635}\right)\left({552}{,}{618}\right)\left({554}{,}{665}\right)\left({555}{,}{673}\right)\left({556}{,}{660}\right)\left({558}{,}{676}\right)\left({560}{,}{679}\right)\left({562}{,}{682}\right)\left({564}{,}{633}\right)\left({566}{,}{658}\right)\left({567}{,}{613}\right)\left({570}{,}{688}\right)\left({572}{,}{666}\right)\left({575}{,}{693}\right)\left({577}{,}{694}\right)\left({580}{,}{697}\right)\left({582}{,}{698}\right)\left({583}{,}{639}\right)\left({587}{,}{683}\right)\left({590}{,}{704}\right)\left({593}{,}{663}\right)\left({597}{,}{691}\right)\left({598}{,}{702}\right)\left({599}{,}{709}\right)\left({605}{,}{715}\right)\left({607}{,}{717}\right)\left({610}{,}{687}\right)\left({611}{,}{720}\right)\left({615}{,}{723}\right)\left({617}{,}{669}\right)\left({622}{,}{727}\right)\left({624}{,}{728}\right)\left({626}{,}{675}\right)\left({627}{,}{730}\right)\left({630}{,}{732}\right)\left({636}{,}{648}\right)\left({637}{,}{736}\right)\left({642}{,}{664}\right)\left({644}{,}{655}\right)\left({645}{,}{722}\right)\left({646}{,}{672}\right)\left({649}{,}{745}\right)\left({650}{,}{746}\right)\left({652}{,}{716}\right)\left({656}{,}{749}\right)\left({662}{,}{701}\right)\left({667}{,}{708}\right)\left({668}{,}{754}\right)\left({670}{,}{707}\right)\left({671}{,}{695}\right)\left({674}{,}{719}\right)\left({677}{,}{755}\right)\left({678}{,}{737}\right)\left({680}{,}{726}\right)\left({684}{,}{706}\right)\left({685}{,}{765}\right)\left({686}{,}{767}\right)\left({689}{,}{770}\right)\left({692}{,}{773}\right)\left({696}{,}{775}\right)\left({699}{,}{712}\right)\left({700}{,}{739}\right)\left({703}{,}{778}\right)\left({705}{,}{763}\right)\left({710}{,}{782}\right)\left({711}{,}{783}\right)\left({713}{,}{784}\right)\left({714}{,}{785}\right)\left({718}{,}{786}\right)\left({721}{,}{789}\right)\left({724}{,}{791}\right)\left({725}{,}{757}\right)\left({729}{,}{793}\right)\left({731}{,}{794}\right)\left({733}{,}{760}\right)\left({734}{,}{795}\right)\left({735}{,}{787}\right)\left({738}{,}{798}\right)\left({740}{,}{799}\right)\left({741}{,}{801}\right)\left({742}{,}{753}\right)\left({743}{,}{744}\right)\left({747}{,}{796}\right)\left({748}{,}{756}\right)\left({750}{,}{772}\right)\left({751}{,}{804}\right)\left({752}{,}{805}\right)\left({758}{,}{780}\right)\left({759}{,}{777}\right)\left({761}{,}{766}\right)\left({762}{,}{807}\right)\left({764}{,}{790}\right)\left({768}{,}{808}\right)\left({769}{,}{809}\right)\left({771}{,}{810}\right)\left({774}{,}{797}\right)\left({776}{,}{800}\right)\left({779}{,}{788}\right)\left({781}{,}{812}\right)\left({792}{,}{816}\right)\left({802}{,}{817}\right)\left({803}{,}{811}\right)\left({806}{,}{815}\right)\left({813}{,}{818}\right)\left({814}{,}{819}\right){,}\left({1}{,}{3}{,}{6}{,}{11}{,}{19}{,}{32}{,}{51}{,}{79}{,}{122}\right)\left({2}{,}{4}{,}{8}{,}{14}{,}{24}{,}{39}{,}{61}{,}{95}{,}{147}\right)\left({5}{,}{9}{,}{16}{,}{27}{,}{43}{,}{68}{,}{67}{,}{102}{,}{157}\right)\left({7}{,}{12}{,}{21}\right)\left({10}{,}{17}{,}{29}{,}{46}{,}{72}{,}{110}{,}{166}{,}{248}{,}{355}\right)\left({13}{,}{22}{,}{36}{,}{56}{,}{87}{,}{134}{,}{201}{,}{294}{,}{414}\right)\left({15}{,}{25}{,}{40}{,}{63}{,}{97}{,}{149}{,}{223}{,}{324}{,}{109}\right)\left({18}{,}{30}{,}{48}{,}{75}{,}{115}{,}{172}{,}{256}{,}{368}{,}{446}\right)\left({20}{,}{33}{,}{52}{,}{81}{,}{125}{,}{187}{,}{278}{,}{89}{,}{137}\right)\left({23}{,}{37}{,}{58}{,}{90}{,}{139}{,}{208}{,}{179}{,}{267}{,}{380}\right)\left({26}{,}{41}{,}{65}{,}{100}{,}{153}{,}{230}{,}{333}{,}{460}{,}{595}\right)\left({28}{,}{44}{,}{69}{,}{105}{,}{160}{,}{240}{,}{260}{,}{71}{,}{108}\right)\left({31}{,}{49}{,}{76}{,}{117}{,}{175}{,}{261}{,}{361}{,}{482}{,}{62}\right)\left({34}{,}{53}{,}{83}{,}{128}{,}{191}{,}{282}{,}{257}{,}{369}{,}{489}\right)\left({35}{,}{54}{,}{84}{,}{130}{,}{194}{,}{285}{,}{182}{,}{271}{,}{386}\right)\left({38}{,}{59}{,}{92}{,}{142}{,}{213}{,}{167}{,}{249}{,}{357}{,}{354}\right)\left({42}{,}{66}{,}{101}{,}{155}{,}{233}{,}{337}{,}{106}{,}{161}{,}{242}\right)\left({45}{,}{70}{,}{107}{,}{163}{,}{245}{,}{350}{,}{475}{,}{255}{,}{366}\right)\left({47}{,}{73}{,}{112}{,}{168}{,}{251}{,}{360}{,}{481}{,}{613}{,}{722}\right)\left({50}{,}{77}{,}{119}{,}{178}{,}{266}{,}{159}{,}{238}{,}{342}{,}{466}\right)\left({55}{,}{85}{,}{132}{,}{197}{,}{224}{,}{156}{,}{234}{,}{300}{,}{423}\right)\left({57}{,}{88}{,}{136}{,}{204}{,}{298}{,}{420}{,}{437}{,}{564}{,}{684}\right)\left({60}{,}{93}{,}{144}{,}{216}{,}{314}{,}{438}{,}{566}{,}{686}{,}{768}\right)\left({64}{,}{98}{,}{150}{,}{225}{,}{326}{,}{451}{,}{582}{,}{604}{,}{714}\right)\left({74}{,}{113}{,}{138}{,}{206}{,}{301}{,}{424}{,}{547}{,}{608}{,}{719}\right)\left({78}{,}{120}{,}{180}{,}{268}{,}{381}{,}{498}{,}{626}{,}{359}{,}{462}\right)\left({80}{,}{123}{,}{184}{,}{274}{,}{389}{,}{509}{,}{635}{,}{253}{,}{363}\right)\left({82}{,}{126}{,}{189}{,}{280}{,}{395}{,}{517}{,}{643}{,}{325}{,}{235}\right)\left({86}{,}{133}{,}{199}{,}{291}{,}{409}{,}{530}{,}{183}{,}{272}{,}{310}\right)\left({91}{,}{140}{,}{210}{,}{306}{,}{269}{,}{382}{,}{500}{,}{413}{,}{448}\right)\left({94}{,}{145}{,}{218}{,}{317}{,}{442}{,}{572}{,}{307}{,}{430}{,}{554}\right)\left({96}{,}{121}{,}{181}{,}{270}{,}{384}{,}{503}{,}{399}{,}{520}{,}{645}\right)\left({99}{,}{151}{,}{227}{,}{329}{,}{200}{,}{292}{,}{411}{,}{533}{,}{103}\right)\left({104}{,}{158}{,}{237}{,}{340}{,}{464}{,}{597}{,}{124}{,}{185}{,}{276}\right)\left({111}{,}{131}{,}{195}{,}{286}{,}{402}{,}{523}{,}{648}{,}{744}{,}{732}\right)\left({114}{,}{170}{,}{164}{,}{246}{,}{352}{,}{471}{,}{452}{,}{583}{,}{699}\right)\left({116}{,}{173}{,}{258}{,}{370}{,}{379}{,}{196}{,}{287}{,}{404}{,}{502}\right)\left({118}{,}{176}{,}{263}{,}{375}{,}{346}{,}{273}{,}{388}{,}{507}{,}{236}\right)\left({127}{,}{177}{,}{264}{,}{377}{,}{406}{,}{527}{,}{653}{,}{647}{,}{743}\right)\left({129}{,}{192}{,}{174}{,}{259}{,}{372}{,}{436}{,}{563}{,}{683}{,}{764}\right)\left({135}{,}{202}{,}{229}{,}{332}{,}{459}{,}{593}{,}{706}{,}{478}{,}{165}\right)\left({141}{,}{211}{,}{308}{,}{431}{,}{555}{,}{674}{,}{760}{,}{783}{,}{673}\right)\left({143}{,}{214}{,}{312}{,}{435}{,}{562}{,}{467}{,}{599}{,}{710}{,}{186}\right)\left({146}{,}{219}{,}{319}{,}{445}{,}{577}{,}{621}{,}{344}{,}{468}{,}{600}\right)\left({148}{,}{221}{,}{322}{,}{449}{,}{580}{,}{651}{,}{364}{,}{485}{,}{303}\right)\left({152}{,}{228}{,}{331}{,}{458}{,}{592}{,}{499}{,}{627}{,}{731}{,}{717}\right)\left({154}{,}{231}{,}{335}{,}{339}{,}{367}{,}{486}{,}{617}{,}{497}{,}{624}\right)\left({162}{,}{243}{,}{347}{,}{470}{,}{429}{,}{450}{,}{484}{,}{615}{,}{724}\right)\left({169}{,}{252}{,}{362}{,}{483}{,}{349}{,}{473}{,}{605}{,}{581}{,}{474}\right)\left({171}{,}{254}{,}{365}{,}{262}{,}{374}{,}{493}{,}{622}{,}{586}{,}{701}\right)\left({188}{,}{279}{,}{394}{,}{283}{,}{398}{,}{519}{,}{594}{,}{707}{,}{629}\right)\left({190}{,}{193}{,}{284}{,}{400}{,}{522}{,}{232}{,}{207}{,}{302}{,}{425}\right)\left({198}{,}{289}{,}{239}{,}{343}{,}{265}{,}{378}{,}{492}{,}{222}{,}{323}\right)\left({203}{,}{296}{,}{417}{,}{541}{,}{664}{,}{755}{,}{328}{,}{454}{,}{587}\right)\left({205}{,}{299}{,}{422}{,}{457}{,}{455}{,}{588}{,}{702}{,}{463}{,}{373}\right)\left({209}{,}{304}{,}{427}{,}{550}{,}{250}{,}{358}{,}{247}{,}{353}{,}{477}\right)\left({212}{,}{309}{,}{433}{,}{558}{,}{677}{,}{602}{,}{712}{,}{606}{,}{716}\right)\left({215}{,}{313}{,}{341}{,}{290}{,}{407}{,}{496}{,}{488}{,}{618}{,}{403}\right)\left({217}{,}{315}{,}{440}{,}{444}{,}{575}{,}{679}{,}{534}{,}{659}{,}{752}\right)\left({220}{,}{320}{,}{351}{,}{387}{,}{505}{,}{416}{,}{539}{,}{662}{,}{754}\right)\left({226}{,}{327}{,}{453}{,}{585}{,}{700}{,}{777}{,}{808}{,}{579}{,}{696}\right)\left({241}{,}{345}{,}{469}{,}{601}{,}{711}{,}{356}{,}{479}{,}{610}{,}{576}\right)\left({244}{,}{348}{,}{472}{,}{603}{,}{713}{,}{775}{,}{786}{,}{549}{,}{669}\right)\left({275}{,}{390}{,}{511}{,}{637}{,}{737}{,}{778}{,}{559}{,}{678}{,}{762}\right)\left({277}{,}{392}{,}{514}{,}{642}{,}{741}{,}{297}{,}{418}{,}{542}{,}{665}\right)\left({281}{,}{396}{,}{397}{,}{518}{,}{644}{,}{536}{,}{421}{,}{545}{,}{516}\right)\left({288}{,}{405}{,}{526}{,}{652}{,}{748}{,}{791}{,}{694}{,}{321}{,}{447}\right)\left({293}{,}{412}{,}{535}{,}{660}{,}{753}{,}{439}{,}{567}{,}{383}{,}{501}\right)\left({295}{,}{415}{,}{538}{,}{540}{,}{663}{,}{619}{,}{725}{,}{792}{,}{789}\right)\left({305}{,}{428}{,}{552}{,}{671}{,}{759}{,}{785}{,}{401}{,}{338}{,}{336}\right)\left({311}{,}{434}{,}{560}{,}{680}{,}{763}{,}{318}{,}{443}{,}{574}{,}{692}\right)\left({316}{,}{441}{,}{570}{,}{689}{,}{771}{,}{784}{,}{814}{,}{697}{,}{776}\right)\left({330}{,}{456}{,}{590}{,}{596}{,}{708}{,}{730}{,}{782}{,}{813}{,}{804}\right)\left({334}{,}{461}{,}{408}{,}{528}{,}{655}{,}{578}{,}{695}{,}{510}{,}{636}\right)\left({371}{,}{490}{,}{620}{,}{726}{,}{521}{,}{646}{,}{742}{,}{802}{,}{584}\right)\left({376}{,}{494}{,}{623}{,}{682}{,}{727}{,}{591}{,}{705}{,}{780}{,}{811}\right)\left({385}{,}{504}{,}{630}{,}{733}{,}{551}{,}{670}{,}{614}{,}{723}{,}{487}\right)\left({391}{,}{512}{,}{639}{,}{532}{,}{557}{,}{675}{,}{513}{,}{640}{,}{739}\right)\left({393}{,}{515}{,}{569}{,}{657}{,}{750}{,}{628}{,}{632}{,}{571}{,}{690}\right)\left({410}{,}{531}{,}{658}{,}{751}{,}{537}{,}{508}{,}{633}{,}{491}{,}{506}\right)\left({419}{,}{543}{,}{666}{,}{756}{,}{616}{,}{561}{,}{681}{,}{544}{,}{661}\right)\left({426}{,}{548}{,}{668}{,}{758}{,}{806}{,}{654}{,}{495}{,}{465}{,}{598}\right)\left({432}{,}{556}{,}{480}{,}{611}{,}{546}{,}{667}{,}{757}{,}{529}{,}{656}\right)\left({476}{,}{607}{,}{718}{,}{787}{,}{815}{,}{816}{,}{568}{,}{687}{,}{769}\right)\left({524}{,}{649}{,}{612}{,}{721}{,}{790}{,}{638}{,}{738}{,}{794}{,}{773}\right)\left({525}{,}{650}{,}{747}{,}{704}{,}{779}{,}{693}{,}{774}{,}{688}{,}{728}\right)\left({553}{,}{672}{,}{609}{,}{573}{,}{691}{,}{772}{,}{745}{,}{589}{,}{703}\right)\left({565}{,}{685}{,}{766}{,}{805}{,}{736}{,}{797}{,}{749}{,}{631}{,}{734}\right)\left({625}{,}{729}{,}{676}{,}{761}{,}{799}{,}{746}{,}{803}{,}{709}{,}{781}\right)\left({634}{,}{735}{,}{796}{,}{807}{,}{818}{,}{810}{,}{765}{,}{801}{,}{795}\right)\left({641}{,}{740}{,}{800}{,}{817}{,}{798}{,}{812}{,}{770}{,}{767}{,}{715}\right)\left({720}{,}{788}{,}{809}\right)⟩$ (1)
 > $\mathrm{GroupOrder}\left(G\right)$
 ${211341312}$ (2)
 > $\mathrm{Degree}\left(G\right)$
 ${819}$ (3)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{IsPrimitive}\left(G\right)$
 ${\mathrm{true}}$ (5)
 > $G≔\mathrm{Steinberg3D4}\left(3\right):$
 > $\mathrm{Degree}\left(G\right)$
 ${26572}$ (6)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{true}}$ (7)
 > $\mathrm{IsSimple}\left(\mathrm{Steinberg3D4}\left(4096\right)\right)$
 ${\mathrm{true}}$ (8)
 > $\mathrm{GroupOrder}\left(\mathrm{Steinberg3D4}\left(27\right)\right)$
 ${11956114445971661401099296184508431605312}$ (9)
 > $\mathrm{ClassNumber}\left(\mathrm{Steinberg3D4}\left(32\right)\right)$
 ${1082405}$ (10)
 > $G≔\mathrm{Steinberg3D4}\left(q\right)$
 ${G}{≔}{}^{{3}}{D}_{{4}}{}\left({q}\right)$ (11)
 > $\mathrm{ClassNumber}\left(G\right)$
 ${{q}}^{{4}}{+}{{q}}^{{3}}{+}{{q}}^{{2}}{+}{q}{+}{5}{+}{\mathrm{irem}}{}\left({q}{,}{2}\right)$ (12)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{true}}$ (13)
 Compatibility