SymplecticGroup - Maple Help

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GroupTheory

 SymplecticGroup
 construct a permutation group isomorphic to a symplectic group

 Calling Sequence SymplecticGroup(n, q) Sp(n, q)

Parameters

 n - an even positive integer q - power of a prime number

Description

 • The symplectic group $Sp\left(n,q\right)$ is the group of all $n×n$ matrices over the field with $q$ elements that respect a fixed nondegenerate symplectic form. The integer $n$ must be even.
 • The SymplecticGroup( n, q ) command returns a permutation group isomorphic to the symplectic group $Sp\left(n,q\right)$ .
 • Note that for $n=2$ the groups $Sp\left(n,q\right)$ and $SL\left(n,q\right)$ are isomorphic, so that a special linear group is returned in this case.
 • If either, or both, of n and q is non-numeric, then a symbolic group representing the symplectic group is returned.
 • The Sp( n, q ) command is provided as an abbreviation.
 • In the Standard Worksheet interface, you can insert this group into a document or worksheet by using the Group Constructors palette.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{SymplecticGroup}\left(4,5\right)$
 ${G}{≔}{\mathbf{Sp}}\left({4}{,}{5}\right)$ (1)
 > $\mathrm{ifactor}\left(\mathrm{GroupOrder}\left(G\right)\right)$
 ${\left({2}\right)}^{{7}}{}{\left({3}\right)}^{{2}}{}{\left({5}\right)}^{{4}}{}\left({13}\right)$ (2)
 > $\mathrm{GroupOrder}\left(\mathrm{SylowSubgroup}\left(2,G\right)\right)$
 ${128}$ (3)
 > $\mathrm{S3}≔\mathrm{SylowSubgroup}\left(3,G\right)$
 ${\mathrm{S3}}{≔}⟨\left({1}{,}{119}{,}{168}\right)\left({2}{,}{160}{,}{261}\right)\left({3}{,}{24}{,}{272}\right)\left({4}{,}{253}{,}{193}\right)\left({5}{,}{30}{,}{205}\right)\left({6}{,}{305}{,}{265}\right)\left({7}{,}{185}{,}{127}\right)\left({8}{,}{46}{,}{143}\right)\left({9}{,}{415}{,}{197}\right)\left({10}{,}{245}{,}{174}\right)\left({11}{,}{390}{,}{510}\right)\left({12}{,}{34}{,}{181}\right)\left({13}{,}{338}{,}{134}\right)\left({14}{,}{342}{,}{474}\right)\left({15}{,}{309}{,}{444}\right)\left({16}{,}{220}{,}{300}\right)\left({17}{,}{622}{,}{406}\right)\left({18}{,}{249}{,}{375}\right)\left({19}{,}{287}{,}{410}\right)\left({20}{,}{621}{,}{327}\right)\left({21}{,}{323}{,}{240}\right)\left({22}{,}{623}{,}{294}\right)\left({23}{,}{436}{,}{437}\right)\left({25}{,}{487}{,}{416}\right)\left({27}{,}{403}{,}{333}\right)\left({28}{,}{624}{,}{230}\right)\left({29}{,}{535}{,}{536}\right)\left({31}{,}{547}{,}{339}\right)\left({33}{,}{365}{,}{366}\right)\left({35}{,}{558}{,}{306}\right)\left({37}{,}{528}{,}{549}\right)\left({38}{,}{552}{,}{397}\right)\left({39}{,}{100}{,}{277}\right)\left({40}{,}{44}{,}{505}\right)\left({41}{,}{386}{,}{244}\right)\left({42}{,}{120}{,}{564}\right)\left({43}{,}{341}{,}{496}\right)\left({45}{,}{470}{,}{471}\right)\left({47}{,}{506}{,}{246}\right)\left({49}{,}{458}{,}{576}\right)\left({50}{,}{488}{,}{316}\right)\left({51}{,}{155}{,}{394}\right)\left({52}{,}{56}{,}{557}\right)\left({53}{,}{450}{,}{304}\right)\left({54}{,}{161}{,}{578}\right)\left({55}{,}{248}{,}{551}\right)\left({57}{,}{424}{,}{493}\right)\left({58}{,}{497}{,}{280}\right)\left({59}{,}{78}{,}{210}\right)\left({60}{,}{64}{,}{546}\right)\left({61}{,}{481}{,}{337}\right)\left({62}{,}{186}{,}{520}\right)\left({63}{,}{371}{,}{572}\right)\left({65}{,}{446}{,}{132}\right)\left({66}{,}{115}{,}{494}\right)\left({67}{,}{94}{,}{154}\right)\left({68}{,}{542}{,}{519}\right)\left({69}{,}{554}{,}{504}\right)\left({70}{,}{183}{,}{178}\right)\left({71}{,}{99}{,}{104}\right)\left({72}{,}{571}{,}{545}\right)\left({73}{,}{267}{,}{585}\right)\left({74}{,}{562}{,}{236}\right)\left({75}{,}{184}{,}{241}\right)\left({76}{,}{77}{,}{146}\right)\left({79}{,}{550}{,}{89}\right)\left({80}{,}{351}{,}{511}\right)\left({81}{,}{503}{,}{213}\right)\left({82}{,}{114}{,}{313}\right)\left({83}{,}{87}{,}{486}\right)\left({84}{,}{517}{,}{414}\right)\left({85}{,}{254}{,}{518}\right)\left({86}{,}{308}{,}{603}\right)\left({88}{,}{382}{,}{172}\right)\left({90}{,}{112}{,}{113}\right)\left({91}{,}{480}{,}{563}\right)\left({92}{,}{589}{,}{556}\right)\left({93}{,}{117}{,}{269}\right)\left({95}{,}{495}{,}{484}\right)\left({96}{,}{200}{,}{580}\right)\left({97}{,}{516}{,}{225}\right)\left({98}{,}{118}{,}{301}\right)\left({101}{,}{593}{,}{145}\right)\left({102}{,}{377}{,}{196}\right)\left({103}{,}{156}{,}{570}\right)\left({105}{,}{449}{,}{579}\right)\left({106}{,}{499}{,}{575}\right)\left({107}{,}{251}{,}{140}\right)\left({108}{,}{560}{,}{453}\right)\left({109}{,}{176}{,}{565}\right)\left({110}{,}{514}{,}{331}\right)\left({111}{,}{252}{,}{334}\right)\left({116}{,}{328}{,}{303}\right)\left({121}{,}{608}{,}{619}\right)\left({122}{,}{123}{,}{137}\right)\left({124}{,}{322}{,}{356}\right)\left({126}{,}{601}{,}{399}\right)\left({128}{,}{538}{,}{307}\right)\left({129}{,}{163}{,}{164}\right)\left({131}{,}{490}{,}{302}\right)\left({133}{,}{256}{,}{257}\right)\left({135}{,}{472}{,}{485}\right)\left({136}{,}{443}{,}{247}\right)\left({138}{,}{521}{,}{151}\right)\left({139}{,}{569}{,}{553}\right)\left({141}{,}{457}{,}{289}\right)\left({142}{,}{422}{,}{476}\right)\left({144}{,}{372}{,}{264}\right)\left({147}{,}{385}{,}{605}\right)\left({148}{,}{574}{,}{604}\right)\left({149}{,}{158}{,}{202}\right)\left({150}{,}{512}{,}{389}\right)\left({152}{,}{509}{,}{292}\right)\left({153}{,}{159}{,}{411}\right)\left({157}{,}{231}{,}{413}\right)\left({162}{,}{615}{,}{618}\right)\left({165}{,}{219}{,}{429}\right)\left({167}{,}{612}{,}{318}\right)\left({169}{,}{473}{,}{417}\right)\left({171}{,}{508}{,}{412}\right)\left({173}{,}{188}{,}{189}\right)\left({175}{,}{373}{,}{391}\right)\left({177}{,}{491}{,}{588}\right)\left({179}{,}{350}{,}{332}\right)\left({180}{,}{526}{,}{378}\right)\left({182}{,}{407}{,}{243}\right)\left({187}{,}{586}{,}{616}\right)\left({190}{,}{402}{,}{463}\right)\left({192}{,}{587}{,}{282}\right)\left({195}{,}{561}{,}{242}\right)\left({198}{,}{537}{,}{525}\right)\left({199}{,}{374}{,}{340}\right)\left({201}{,}{602}{,}{498}\right)\left({203}{,}{527}{,}{222}\right)\left({204}{,}{349}{,}{421}\right)\left({206}{,}{440}{,}{577}\right)\left({207}{,}{529}{,}{597}\right)\left({208}{,}{568}{,}{404}\right)\left({209}{,}{600}{,}{435}\right)\left({211}{,}{357}{,}{279}\right)\left({212}{,}{314}{,}{464}\right)\left({215}{,}{260}{,}{590}\right)\left({216}{,}{228}{,}{355}\right)\left({217}{,}{293}{,}{461}\right)\left({218}{,}{433}{,}{347}\right)\left({221}{,}{428}{,}{283}\right)\left({223}{,}{346}{,}{582}\right)\left({224}{,}{380}{,}{507}\right)\left({226}{,}{468}{,}{383}\right)\left({227}{,}{352}{,}{500}\right)\left({229}{,}{530}{,}{320}\right)\left({232}{,}{344}{,}{598}\right)\left({233}{,}{362}{,}{381}\right)\left({234}{,}{425}{,}{466}\right)\left({235}{,}{539}{,}{555}\right)\left({237}{,}{534}{,}{441}\right)\left({238}{,}{459}{,}{432}\right)\left({239}{,}{270}{,}{423}\right)\left({250}{,}{295}{,}{336}\right)\left({255}{,}{599}{,}{617}\right)\left({258}{,}{286}{,}{532}\right)\left({263}{,}{513}{,}{335}\right)\left({266}{,}{442}{,}{454}\right)\left({268}{,}{548}{,}{573}\right)\left({271}{,}{456}{,}{348}\right)\left({273}{,}{478}{,}{515}\right)\left({274}{,}{460}{,}{610}\right)\left({275}{,}{606}{,}{324}\right)\left({276}{,}{581}{,}{455}\right)\left({278}{,}{430}{,}{396}\right)\left({284}{,}{405}{,}{354}\right)\left({285}{,}{501}{,}{420}\right)\left({288}{,}{531}{,}{400}\right)\left({290}{,}{311}{,}{524}\right)\left({291}{,}{369}{,}{559}\right)\left({296}{,}{419}{,}{611}\right)\left({297}{,}{434}{,}{370}\right)\left({298}{,}{492}{,}{359}\right)\left({299}{,}{475}{,}{523}\right)\left({310}{,}{426}{,}{594}\right)\left({312}{,}{566}{,}{364}\right)\left({315}{,}{395}{,}{489}\right)\left({319}{,}{325}{,}{462}\right)\left({321}{,}{360}{,}{363}\right)\left({326}{,}{427}{,}{401}\right)\left({329}{,}{439}{,}{595}\right)\left({330}{,}{445}{,}{502}\right)\left({343}{,}{584}{,}{465}\right)\left({345}{,}{393}{,}{522}\right)\left({353}{,}{614}{,}{392}\right)\left({358}{,}{418}{,}{607}\right)\left({361}{,}{467}{,}{469}\right)\left({367}{,}{583}{,}{431}\right)\left({368}{,}{596}{,}{408}\right)\left({376}{,}{567}{,}{409}\right)\left({384}{,}{592}{,}{387}\right)\left({438}{,}{591}{,}{533}\right)\left({448}{,}{609}{,}{451}\right)\left({479}{,}{613}{,}{482}\right)\left({541}{,}{620}{,}{543}\right){,}\left({1}{,}{162}{,}{372}\right)\left({2}{,}{255}{,}{377}\right)\left({3}{,}{427}{,}{468}\right)\left({4}{,}{187}{,}{446}\right)\left({5}{,}{530}{,}{362}\right)\left({6}{,}{213}{,}{561}\right)\left({7}{,}{121}{,}{382}\right)\left({8}{,}{461}{,}{434}\right)\left({9}{,}{280}{,}{490}\right)\left({10}{,}{316}{,}{513}\right)\left({11}{,}{580}{,}{225}\right)\left({12}{,}{354}{,}{534}\right)\left({13}{,}{397}{,}{508}\right)\left({14}{,}{521}{,}{292}\right)\left({15}{,}{585}{,}{236}\right)\left({16}{,}{51}{,}{103}\right)\left({17}{,}{611}{,}{139}\right)\left({18}{,}{565}{,}{331}\right)\left({19}{,}{82}{,}{66}\right)\left({20}{,}{596}{,}{177}\right)\left({21}{,}{39}{,}{145}\right)\left({22}{,}{598}{,}{201}\right)\left({23}{,}{542}{,}{507}\right)\left({24}{,}{401}{,}{383}\right)\left({25}{,}{575}{,}{157}\right)\left({26}{,}{194}{,}{483}\right)\left({27}{,}{59}{,}{89}\right)\left({28}{,}{595}{,}{268}\right)\left({29}{,}{480}{,}{559}\right)\left({30}{,}{320}{,}{381}\right)\left({31}{,}{504}{,}{250}\right)\left({32}{,}{130}{,}{388}\right)\left({33}{,}{449}{,}{515}\right)\left({34}{,}{284}{,}{441}\right)\left({35}{,}{604}{,}{116}\right)\left({36}{,}{262}{,}{544}\right)\left({37}{,}{163}{,}{312}\right)\left({38}{,}{412}{,}{338}\right)\left({40}{,}{505}{,}{44}\right)\left({41}{,}{592}{,}{98}\right)\left({42}{,}{584}{,}{560}\right)\left({43}{,}{288}{,}{467}\right)\left({45}{,}{385}{,}{577}\right)\left({46}{,}{217}{,}{370}\right)\left({47}{,}{556}{,}{182}\right)\left({48}{,}{170}{,}{452}\right)\left({49}{,}{256}{,}{209}\right)\left({50}{,}{335}{,}{245}\right)\left({52}{,}{557}{,}{56}\right)\left({53}{,}{609}{,}{153}\right)\left({54}{,}{607}{,}{571}\right)\left({55}{,}{325}{,}{360}\right)\left({57}{,}{122}{,}{393}\right)\left({58}{,}{302}{,}{415}\right)\left({60}{,}{546}{,}{64}\right)\left({61}{,}{613}{,}{75}\right)\left({62}{,}{591}{,}{512}\right)\left({63}{,}{221}{,}{501}\right)\left({65}{,}{193}{,}{616}\right)\left({67}{,}{421}{,}{466}\right)\left({68}{,}{380}{,}{437}\right)\left({69}{,}{295}{,}{547}\right)\left({70}{,}{612}{,}{199}\right)\left({71}{,}{271}{,}{227}\right)\left({72}{,}{578}{,}{418}\right)\left({73}{,}{74}{,}{309}\right)\left({76}{,}{180}{,}{238}\right)\left({77}{,}{526}{,}{459}\right)\left({78}{,}{79}{,}{403}\right)\left({80}{,}{188}{,}{276}\right)\left({81}{,}{242}{,}{305}\right)\left({83}{,}{486}{,}{87}\right)\left({84}{,}{620}{,}{111}\right)\left({85}{,}{583}{,}{495}\right)\left({86}{,}{228}{,}{433}\right)\left({88}{,}{127}{,}{619}\right)\left({90}{,}{476}{,}{359}\right)\left({91}{,}{369}{,}{536}\right)\left({92}{,}{407}{,}{506}\right)\left({93}{,}{590}{,}{136}\right)\left({94}{,}{204}{,}{234}\right)\left({95}{,}{518}{,}{367}\right)\left({96}{,}{97}{,}{390}\right)\left({99}{,}{456}{,}{352}\right)\left({100}{,}{101}{,}{323}\right)\left({102}{,}{261}{,}{617}\right)\left({104}{,}{348}{,}{500}\right)\left({105}{,}{478}{,}{366}\right)\left({106}{,}{231}{,}{487}\right)\left({107}{,}{601}{,}{169}\right)\left({108}{,}{564}{,}{343}\right)\left({109}{,}{110}{,}{249}\right)\left({112}{,}{142}{,}{298}\right)\left({113}{,}{422}{,}{492}\right)\left({114}{,}{115}{,}{287}\right)\left({117}{,}{215}{,}{443}\right)\left({118}{,}{386}{,}{387}\right)\left({119}{,}{615}{,}{264}\right)\left({120}{,}{465}{,}{453}\right)\left({123}{,}{522}{,}{424}\right)\left({124}{,}{315}{,}{289}\right)\left({125}{,}{214}{,}{540}\right)\left({126}{,}{417}{,}{140}\right)\left({128}{,}{149}{,}{587}\right)\left({129}{,}{364}{,}{549}\right)\left({131}{,}{197}{,}{497}\right)\left({132}{,}{253}{,}{586}\right)\left({133}{,}{435}{,}{576}\right)\left({134}{,}{552}{,}{171}\right)\left({135}{,}{324}{,}{610}\right)\left({137}{,}{345}{,}{493}\right)\left({138}{,}{509}{,}{474}\right)\left({141}{,}{322}{,}{395}\right)\left({143}{,}{293}{,}{297}\right)\left({144}{,}{168}{,}{618}\right)\left({146}{,}{378}{,}{432}\right)\left({147}{,}{440}{,}{471}\right)\left({148}{,}{328}{,}{558}\right)\left({150}{,}{520}{,}{438}\right)\left({151}{,}{152}{,}{342}\right)\left({154}{,}{349}{,}{425}\right)\left({155}{,}{156}{,}{220}\right)\left({158}{,}{282}{,}{538}\right)\left({159}{,}{450}{,}{451}\right)\left({160}{,}{599}{,}{196}\right)\left({161}{,}{358}{,}{545}\right)\left({164}{,}{566}{,}{528}\right)\left({165}{,}{212}{,}{332}\right)\left({166}{,}{281}{,}{477}\right)\left({167}{,}{340}{,}{178}\right)\left({172}{,}{185}{,}{608}\right)\left({173}{,}{455}{,}{511}\right)\left({174}{,}{488}{,}{263}\right)\left({175}{,}{223}{,}{614}\right)\left({176}{,}{514}{,}{375}\right)\left({179}{,}{219}{,}{314}\right)\left({181}{,}{405}{,}{237}\right)\left({183}{,}{318}{,}{374}\right)\left({184}{,}{481}{,}{482}\right)\left({186}{,}{533}{,}{389}\right)\left({189}{,}{581}{,}{351}\right)\left({190}{,}{396}{,}{222}\right)\left({191}{,}{317}{,}{447}\right)\left({192}{,}{307}{,}{202}\right)\left({195}{,}{265}{,}{503}\right)\left({198}{,}{404}{,}{597}\right)\left({200}{,}{516}{,}{510}\right)\left({203}{,}{402}{,}{278}\right)\left({205}{,}{229}{,}{233}\right)\left({206}{,}{470}{,}{605}\right)\left({207}{,}{537}{,}{208}\right)\left({210}{,}{550}{,}{333}\right)\left({211}{,}{270}{,}{286}\right)\left({216}{,}{218}{,}{603}\right)\left({224}{,}{436}{,}{519}\right)\left({226}{,}{272}{,}{326}\right)\left({230}{,}{439}{,}{573}\right)\left({232}{,}{602}{,}{623}\right)\left({235}{,}{555}{,}{539}\right)\left({239}{,}{258}{,}{279}\right)\left({240}{,}{277}{,}{593}\right)\left({241}{,}{337}{,}{479}\right)\left({243}{,}{246}{,}{589}\right)\left({244}{,}{384}{,}{301}\right)\left({247}{,}{269}{,}{260}\right)\left({248}{,}{462}{,}{363}\right)\left({251}{,}{399}{,}{473}\right)\left({252}{,}{517}{,}{543}\right)\left({254}{,}{431}{,}{484}\right)\left({257}{,}{600}{,}{458}\right)\left({259}{,}{398}{,}{379}\right)\left({266}{,}{290}{,}{594}\right)\left({267}{,}{562}{,}{444}\right)\left({273}{,}{365}{,}{579}\right)\left({274}{,}{472}{,}{275}\right)\left({283}{,}{285}{,}{572}\right)\left({291}{,}{535}{,}{563}\right)\left({294}{,}{344}{,}{498}\right)\left({296}{,}{569}{,}{622}\right)\left({299}{,}{523}{,}{475}\right)\left({300}{,}{394}{,}{570}\right)\left({303}{,}{306}{,}{574}\right)\left({304}{,}{448}{,}{411}\right)\left({308}{,}{355}{,}{347}\right)\left({310}{,}{442}{,}{311}\right)\left({313}{,}{494}{,}{410}\right)\left({319}{,}{321}{,}{551}\right)\left({327}{,}{368}{,}{588}\right)\left({329}{,}{548}{,}{624}\right)\left({330}{,}{502}{,}{445}\right)\left({334}{,}{414}{,}{541}\right)\left({336}{,}{339}{,}{554}\right)\left({341}{,}{531}{,}{469}\right)\left({346}{,}{392}{,}{373}\right)\left({350}{,}{429}{,}{464}\right)\left({353}{,}{391}{,}{582}\right)\left({356}{,}{489}{,}{457}\right)\left({357}{,}{423}{,}{532}\right)\left({361}{,}{496}{,}{400}\right)\left({371}{,}{428}{,}{420}\right)\left({376}{,}{409}{,}{567}\right)\left({406}{,}{419}{,}{553}\right)\left({408}{,}{491}{,}{621}\right)\left({413}{,}{416}{,}{499}\right)\left({426}{,}{454}{,}{524}\right)\left({430}{,}{527}{,}{463}\right)\left({460}{,}{485}{,}{606}\right)\left({525}{,}{568}{,}{529}\right)⟩$ (4)
 > $\mathrm{GroupOrder}\left(\mathrm{S3}\right)$
 ${9}$ (5)
 > $\mathrm{IsCyclic}\left(\mathrm{S3}\right)$
 ${\mathrm{false}}$ (6)
 > $\mathrm{IdentifySmallGroup}\left(\mathrm{S3}\right)$
 ${9}{,}{2}$ (7)
 > $\mathrm{GroupOrder}\left(\mathrm{SylowSubgroup}\left(5,G\right)\right)$
 ${625}$ (8)
 > $\mathrm{IsTrivial}\left(\mathrm{PCore}\left(5,G\right)\right)$
 ${\mathrm{true}}$ (9)
 > $\mathrm{GroupOrder}\left(\mathrm{SylowSubgroup}\left(13,G\right)\right)$
 ${13}$ (10)
 > $G≔\mathrm{SymplecticGroup}\left(4,3\right)$
 ${G}{≔}{\mathbf{Sp}}\left({4}{,}{3}\right)$ (11)
 > $\mathrm{Degree}\left(G\right)$
 ${80}$ (12)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{false}}$ (13)
 > $\mathrm{GroupOrder}\left(\mathrm{Centre}\left(G\right)\right)$
 ${2}$ (14)

For $n=2$ the corresponding special linear group is returned.

 > $\mathrm{SymplecticGroup}\left(2,5\right)$
 ${\mathbf{SL}}\left({2}{,}{5}\right)$ (15)

Note the exceptional isomorphism:

 > $\mathrm{AreIsomorphic}\left(\mathrm{SymplecticGroup}\left(4,2\right),\mathrm{Symm}\left(6\right)\right)$
 ${\mathrm{true}}$ (16)
 > $G≔\mathrm{SymplecticGroup}\left(6,q\right)$
 ${G}{≔}{\mathbf{Sp}}\left({6}{,}{q}\right)$ (17)
 > $\mathrm{GroupOrder}\left(G\right)$
 ${{q}}^{{9}}{}\left({{q}}^{{2}}{-}{1}\right){}\left({{q}}^{{4}}{-}{1}\right){}\left({{q}}^{{6}}{-}{1}\right)$ (18)
 > $\mathrm{ClassNumber}\left(\mathrm{SymplecticGroup}\left(8,q\right)\right)$
 $\left\{\begin{array}{cc}{5}{}{q}{+}\left({q}{+}{1}\right){}{q}{+}{4}{}{{q}}^{{2}}{+}\left({{q}}^{{2}}{+}{q}{+}{3}\right){}{q}{+}{{q}}^{{4}}{+}{{q}}^{{3}}{+}{7}& {q}{::}{\mathrm{even}}\\ {25}{}{q}{+}{51}{+}\left({q}{+}{4}\right){}{q}{+}{11}{}{{q}}^{{2}}{+}\left({{q}}^{{2}}{+}{4}{}{q}{+}{10}\right){}{q}{+}{{q}}^{{4}}{+}{4}{}{{q}}^{{3}}& {\mathrm{otherwise}}\end{array}\right\$ (19)
 > $\mathrm{ClassNumber}\left(\mathrm{SymplecticGroup}\left(4,{11}^{k}\right)\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}assuming\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}k::\mathrm{posint}$
 ${5}{}{{11}}^{{k}}{+}{10}{+}{\left({{11}}^{{k}}\right)}^{{2}}$ (20)

Compatibility

 • The GroupTheory[SymplecticGroup] command was introduced in Maple 17.