Properties

Label 252680601600.a
Order \( 2^{20} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 17 \)
Exponent \( 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 \)
Nilpotent no
Solvable no
$\card{G^{\mathrm{ab}}}$ \( 1 \)
$\card{Z(G)}$ 1
$\card{\Aut(G)}$ \( 2^{21} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 17 \)
$\card{\mathrm{Out}(G)}$ \( 2 \cdot 3 \)
Perm deg. $256$
Trans deg. not computed
Rank $2$

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Copy content comment:Construction of abstract group
 
Copy content magma:G := ASL(4,4);
 
Copy content gap:G := Group( (1,2)(3,5)(4,11)(6,15)(7,17)(8,20)(9,12)(10,26)(13,31)(14,23)(16,36)(18,39)(19,43)(21,46)(22,47)(24,27)(25,56)(28,63)(29,65)(30,68)(32,70)(33,44)(34,50)(35,74)(37,81)(38,51)(40,86)(41,89)(42,93)(45,96)(48,84)(49,98)(52,108)(53,111)(54,114)(55,117)(57,122)(58,78)(59,126)(60,128)(61,109)(62,125)(64,137)(66,139)(67,132)(69,145)(71,151)(72,153)(73,155)(75,158)(76,77)(79,152)(80,133)(82,165)(83,163)(85,105)(87,171)(88,176)(90,167)(91,94)(92,120)(95,185)(97,189)(99,100)(101,179)(102,194)(103,115)(104,146)(106,198)(107,129)(110,203)(112,207)(113,123)(116,188)(118,210)(119,136)(121,201)(124,217)(127,184)(130,215)(131,142)(134,221)(135,138)(140,232)(141,235)(143,219)(144,240)(147,154)(148,149)(150,229)(156,244)(157,192)(159,247)(160,178)(161,237)(162,238)(164,202)(166,241)(168,190)(169,172)(170,187)(173,195)(174,196)(175,206)(177,197)(180,208)(181,191)(182,183)(186,254)(193,256)(199,236)(200,252)(204,211)(205,255)(209,218)(212,213)(214,220)(216,248)(222,251)(223,239)(224,234)(225,226)(227,250)(228,243)(230,242)(231,233)(245,253)(246,249), (2,3,5)(4,9,12)(6,14,8)(7,17,19)(10,24,27)(13,29,31)(15,33,34)(18,39,41)(20,38,44)(22,47,49)(23,50,51)(25,55,57)(28,61,63)(30,66,68)(35,73,75)(36,76,77)(37,79,81)(40,84,87)(42,91,94)(45,72,97)(46,99,100)(48,104,105)(52,95,71)(53,110,112)(54,113,115)(56,119,120)(58,107,123)(59,124,127)(60,103,129)(62,131,133)(64,135,138)(67,141,125)(69,145,147)(70,148,149)(74,156,157)(78,114,128)(80,161,132)(82,164,166)(83,167,168)(85,169,171)(86,172,146)(88,175,177)(90,160,179)(92,182,117)(96,186,187)(101,191,190)(102,193,165)(106,197,196)(108,199,200)(111,205,180)(116,203,208)(118,209,211)(121,214,184)(122,183,136)(126,220,222)(130,224,218)(134,219,227)(140,229,233)(142,235,237)(143,238,239)(144,228,232)(150,243,242)(151,245,236)(153,170,246)(155,192,212)(158,213,244)(159,204,234)(162,221,225)(163,181,178)(173,194,241)(174,206,216)(176,198,248)(185,252,253)(188,255,207)(189,249,254)(195,202,256)(201,217,251)(210,247,215)(223,226,250)(230,240,231), (2,4,10,25,56,74,78,36,58,26,35,15,11,16,6)(3,7,18,40,85,170,190,99,178,89,97,50,43,21,8)(5,13,30,67,142,236,243,149,231,139,95,44,65,32,14)(9,22,48,86,173,218,124,204,110,202,151,129,109,52,23)(12,28,62,132,225,197,112,206,127,223,153,113,98,45,20)(17,37,80,131,224,205,175,208,164,247,156,179,93,75,38)(19,42,92,183,126,221,166,227,177,251,245,167,152,71,33)(24,53,84,165,250,186,168,94,184,161,210,244,150,70,54)(27,59,125,219,256,200,228,135,203,172,176,192,101,46,60)(29,64,136,182,111,194,238,193,209,255,246,232,154,72,34)(31,69,146,105,196,222,211,214,239,248,157,229,137,73,51)(39,82,141,234,217,253,233,147,216,122,188,96,128,76,83)(41,88,57,121,215,155,103,47,102,133,226,254,242,148,90)(49,106,120,213,163,81,162,171,187,230,138,220,237,185,107)(55,116,198,158,115,63,134,104,195,252,191,100,140,66,118)(61,130,119,212,240,145,241,235,199,181,91,180,169,189,123)(68,143,87,174,207,249,160,79,159,117,201,108,114,77,144) );
 
Copy content sage:G = PermutationGroup(['(1,2)(3,5)(4,11)(6,15)(7,17)(8,20)(9,12)(10,26)(13,31)(14,23)(16,36)(18,39)(19,43)(21,46)(22,47)(24,27)(25,56)(28,63)(29,65)(30,68)(32,70)(33,44)(34,50)(35,74)(37,81)(38,51)(40,86)(41,89)(42,93)(45,96)(48,84)(49,98)(52,108)(53,111)(54,114)(55,117)(57,122)(58,78)(59,126)(60,128)(61,109)(62,125)(64,137)(66,139)(67,132)(69,145)(71,151)(72,153)(73,155)(75,158)(76,77)(79,152)(80,133)(82,165)(83,163)(85,105)(87,171)(88,176)(90,167)(91,94)(92,120)(95,185)(97,189)(99,100)(101,179)(102,194)(103,115)(104,146)(106,198)(107,129)(110,203)(112,207)(113,123)(116,188)(118,210)(119,136)(121,201)(124,217)(127,184)(130,215)(131,142)(134,221)(135,138)(140,232)(141,235)(143,219)(144,240)(147,154)(148,149)(150,229)(156,244)(157,192)(159,247)(160,178)(161,237)(162,238)(164,202)(166,241)(168,190)(169,172)(170,187)(173,195)(174,196)(175,206)(177,197)(180,208)(181,191)(182,183)(186,254)(193,256)(199,236)(200,252)(204,211)(205,255)(209,218)(212,213)(214,220)(216,248)(222,251)(223,239)(224,234)(225,226)(227,250)(228,243)(230,242)(231,233)(245,253)(246,249)', '(2,3,5)(4,9,12)(6,14,8)(7,17,19)(10,24,27)(13,29,31)(15,33,34)(18,39,41)(20,38,44)(22,47,49)(23,50,51)(25,55,57)(28,61,63)(30,66,68)(35,73,75)(36,76,77)(37,79,81)(40,84,87)(42,91,94)(45,72,97)(46,99,100)(48,104,105)(52,95,71)(53,110,112)(54,113,115)(56,119,120)(58,107,123)(59,124,127)(60,103,129)(62,131,133)(64,135,138)(67,141,125)(69,145,147)(70,148,149)(74,156,157)(78,114,128)(80,161,132)(82,164,166)(83,167,168)(85,169,171)(86,172,146)(88,175,177)(90,160,179)(92,182,117)(96,186,187)(101,191,190)(102,193,165)(106,197,196)(108,199,200)(111,205,180)(116,203,208)(118,209,211)(121,214,184)(122,183,136)(126,220,222)(130,224,218)(134,219,227)(140,229,233)(142,235,237)(143,238,239)(144,228,232)(150,243,242)(151,245,236)(153,170,246)(155,192,212)(158,213,244)(159,204,234)(162,221,225)(163,181,178)(173,194,241)(174,206,216)(176,198,248)(185,252,253)(188,255,207)(189,249,254)(195,202,256)(201,217,251)(210,247,215)(223,226,250)(230,240,231)', '(2,4,10,25,56,74,78,36,58,26,35,15,11,16,6)(3,7,18,40,85,170,190,99,178,89,97,50,43,21,8)(5,13,30,67,142,236,243,149,231,139,95,44,65,32,14)(9,22,48,86,173,218,124,204,110,202,151,129,109,52,23)(12,28,62,132,225,197,112,206,127,223,153,113,98,45,20)(17,37,80,131,224,205,175,208,164,247,156,179,93,75,38)(19,42,92,183,126,221,166,227,177,251,245,167,152,71,33)(24,53,84,165,250,186,168,94,184,161,210,244,150,70,54)(27,59,125,219,256,200,228,135,203,172,176,192,101,46,60)(29,64,136,182,111,194,238,193,209,255,246,232,154,72,34)(31,69,146,105,196,222,211,214,239,248,157,229,137,73,51)(39,82,141,234,217,253,233,147,216,122,188,96,128,76,83)(41,88,57,121,215,155,103,47,102,133,226,254,242,148,90)(49,106,120,213,163,81,162,171,187,230,138,220,237,185,107)(55,116,198,158,115,63,134,104,195,252,191,100,140,66,118)(61,130,119,212,240,145,241,235,199,181,91,180,169,189,123)(68,143,87,174,207,249,160,79,159,117,201,108,114,77,144)'])
 
Copy content sage_gap:G = gap.new('Group( (1,2)(3,5)(4,11)(6,15)(7,17)(8,20)(9,12)(10,26)(13,31)(14,23)(16,36)(18,39)(19,43)(21,46)(22,47)(24,27)(25,56)(28,63)(29,65)(30,68)(32,70)(33,44)(34,50)(35,74)(37,81)(38,51)(40,86)(41,89)(42,93)(45,96)(48,84)(49,98)(52,108)(53,111)(54,114)(55,117)(57,122)(58,78)(59,126)(60,128)(61,109)(62,125)(64,137)(66,139)(67,132)(69,145)(71,151)(72,153)(73,155)(75,158)(76,77)(79,152)(80,133)(82,165)(83,163)(85,105)(87,171)(88,176)(90,167)(91,94)(92,120)(95,185)(97,189)(99,100)(101,179)(102,194)(103,115)(104,146)(106,198)(107,129)(110,203)(112,207)(113,123)(116,188)(118,210)(119,136)(121,201)(124,217)(127,184)(130,215)(131,142)(134,221)(135,138)(140,232)(141,235)(143,219)(144,240)(147,154)(148,149)(150,229)(156,244)(157,192)(159,247)(160,178)(161,237)(162,238)(164,202)(166,241)(168,190)(169,172)(170,187)(173,195)(174,196)(175,206)(177,197)(180,208)(181,191)(182,183)(186,254)(193,256)(199,236)(200,252)(204,211)(205,255)(209,218)(212,213)(214,220)(216,248)(222,251)(223,239)(224,234)(225,226)(227,250)(228,243)(230,242)(231,233)(245,253)(246,249), (2,3,5)(4,9,12)(6,14,8)(7,17,19)(10,24,27)(13,29,31)(15,33,34)(18,39,41)(20,38,44)(22,47,49)(23,50,51)(25,55,57)(28,61,63)(30,66,68)(35,73,75)(36,76,77)(37,79,81)(40,84,87)(42,91,94)(45,72,97)(46,99,100)(48,104,105)(52,95,71)(53,110,112)(54,113,115)(56,119,120)(58,107,123)(59,124,127)(60,103,129)(62,131,133)(64,135,138)(67,141,125)(69,145,147)(70,148,149)(74,156,157)(78,114,128)(80,161,132)(82,164,166)(83,167,168)(85,169,171)(86,172,146)(88,175,177)(90,160,179)(92,182,117)(96,186,187)(101,191,190)(102,193,165)(106,197,196)(108,199,200)(111,205,180)(116,203,208)(118,209,211)(121,214,184)(122,183,136)(126,220,222)(130,224,218)(134,219,227)(140,229,233)(142,235,237)(143,238,239)(144,228,232)(150,243,242)(151,245,236)(153,170,246)(155,192,212)(158,213,244)(159,204,234)(162,221,225)(163,181,178)(173,194,241)(174,206,216)(176,198,248)(185,252,253)(188,255,207)(189,249,254)(195,202,256)(201,217,251)(210,247,215)(223,226,250)(230,240,231), (2,4,10,25,56,74,78,36,58,26,35,15,11,16,6)(3,7,18,40,85,170,190,99,178,89,97,50,43,21,8)(5,13,30,67,142,236,243,149,231,139,95,44,65,32,14)(9,22,48,86,173,218,124,204,110,202,151,129,109,52,23)(12,28,62,132,225,197,112,206,127,223,153,113,98,45,20)(17,37,80,131,224,205,175,208,164,247,156,179,93,75,38)(19,42,92,183,126,221,166,227,177,251,245,167,152,71,33)(24,53,84,165,250,186,168,94,184,161,210,244,150,70,54)(27,59,125,219,256,200,228,135,203,172,176,192,101,46,60)(29,64,136,182,111,194,238,193,209,255,246,232,154,72,34)(31,69,146,105,196,222,211,214,239,248,157,229,137,73,51)(39,82,141,234,217,253,233,147,216,122,188,96,128,76,83)(41,88,57,121,215,155,103,47,102,133,226,254,242,148,90)(49,106,120,213,163,81,162,171,187,230,138,220,237,185,107)(55,116,198,158,115,63,134,104,195,252,191,100,140,66,118)(61,130,119,212,240,145,241,235,199,181,91,180,169,189,123)(68,143,87,174,207,249,160,79,159,117,201,108,114,77,144) )')
 
Copy content oscar:G = @permutation_group(256, (1,2)(3,5)(4,11)(6,15)(7,17)(8,20)(9,12)(10,26)(13,31)(14,23)(16,36)(18,39)(19,43)(21,46)(22,47)(24,27)(25,56)(28,63)(29,65)(30,68)(32,70)(33,44)(34,50)(35,74)(37,81)(38,51)(40,86)(41,89)(42,93)(45,96)(48,84)(49,98)(52,108)(53,111)(54,114)(55,117)(57,122)(58,78)(59,126)(60,128)(61,109)(62,125)(64,137)(66,139)(67,132)(69,145)(71,151)(72,153)(73,155)(75,158)(76,77)(79,152)(80,133)(82,165)(83,163)(85,105)(87,171)(88,176)(90,167)(91,94)(92,120)(95,185)(97,189)(99,100)(101,179)(102,194)(103,115)(104,146)(106,198)(107,129)(110,203)(112,207)(113,123)(116,188)(118,210)(119,136)(121,201)(124,217)(127,184)(130,215)(131,142)(134,221)(135,138)(140,232)(141,235)(143,219)(144,240)(147,154)(148,149)(150,229)(156,244)(157,192)(159,247)(160,178)(161,237)(162,238)(164,202)(166,241)(168,190)(169,172)(170,187)(173,195)(174,196)(175,206)(177,197)(180,208)(181,191)(182,183)(186,254)(193,256)(199,236)(200,252)(204,211)(205,255)(209,218)(212,213)(214,220)(216,248)(222,251)(223,239)(224,234)(225,226)(227,250)(228,243)(230,242)(231,233)(245,253)(246,249), (2,3,5)(4,9,12)(6,14,8)(7,17,19)(10,24,27)(13,29,31)(15,33,34)(18,39,41)(20,38,44)(22,47,49)(23,50,51)(25,55,57)(28,61,63)(30,66,68)(35,73,75)(36,76,77)(37,79,81)(40,84,87)(42,91,94)(45,72,97)(46,99,100)(48,104,105)(52,95,71)(53,110,112)(54,113,115)(56,119,120)(58,107,123)(59,124,127)(60,103,129)(62,131,133)(64,135,138)(67,141,125)(69,145,147)(70,148,149)(74,156,157)(78,114,128)(80,161,132)(82,164,166)(83,167,168)(85,169,171)(86,172,146)(88,175,177)(90,160,179)(92,182,117)(96,186,187)(101,191,190)(102,193,165)(106,197,196)(108,199,200)(111,205,180)(116,203,208)(118,209,211)(121,214,184)(122,183,136)(126,220,222)(130,224,218)(134,219,227)(140,229,233)(142,235,237)(143,238,239)(144,228,232)(150,243,242)(151,245,236)(153,170,246)(155,192,212)(158,213,244)(159,204,234)(162,221,225)(163,181,178)(173,194,241)(174,206,216)(176,198,248)(185,252,253)(188,255,207)(189,249,254)(195,202,256)(201,217,251)(210,247,215)(223,226,250)(230,240,231), (2,4,10,25,56,74,78,36,58,26,35,15,11,16,6)(3,7,18,40,85,170,190,99,178,89,97,50,43,21,8)(5,13,30,67,142,236,243,149,231,139,95,44,65,32,14)(9,22,48,86,173,218,124,204,110,202,151,129,109,52,23)(12,28,62,132,225,197,112,206,127,223,153,113,98,45,20)(17,37,80,131,224,205,175,208,164,247,156,179,93,75,38)(19,42,92,183,126,221,166,227,177,251,245,167,152,71,33)(24,53,84,165,250,186,168,94,184,161,210,244,150,70,54)(27,59,125,219,256,200,228,135,203,172,176,192,101,46,60)(29,64,136,182,111,194,238,193,209,255,246,232,154,72,34)(31,69,146,105,196,222,211,214,239,248,157,229,137,73,51)(39,82,141,234,217,253,233,147,216,122,188,96,128,76,83)(41,88,57,121,215,155,103,47,102,133,226,254,242,148,90)(49,106,120,213,163,81,162,171,187,230,138,220,237,185,107)(55,116,198,158,115,63,134,104,195,252,191,100,140,66,118)(61,130,119,212,240,145,241,235,199,181,91,180,169,189,123)(68,143,87,174,207,249,160,79,159,117,201,108,114,77,144))
 

Group information

Description:$C_2^8.\PSL(4,4)$
Order: \(252680601600\)\(\medspace = 2^{20} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 17 \)
Copy content comment:Order of the group
 
Copy content magma:Order(G);
 
Copy content gap:Order(G);
 
Copy content sage:G.order()
 
Copy content sage_gap:G.Order()
 
Copy content oscar:order(G)
 
Exponent: \(42840\)\(\medspace = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17 \)
Copy content comment:Exponent of the group
 
Copy content magma:Exponent(G);
 
Copy content gap:Exponent(G);
 
Copy content sage:G.exponent()
 
Copy content sage_gap:G.Exponent()
 
Copy content oscar:exponent(G)
 
Automorphism group:$\AGammaL(4,4)$, of order \(1516083609600\)\(\medspace = 2^{21} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 17 \)
Copy content comment:Automorphism group
 
Copy content gap:AutomorphismGroup(G);
 
Copy content magma:AutomorphismGroup(G);
 
Copy content sage:libgap(G).AutomorphismGroup()
 
Copy content sage_gap:G.AutomorphismGroup()
 
Copy content oscar:automorphism_group(G)
 
Composition factors:$C_2$ x 8, $\SL(4,4)$
Copy content comment:Composition factors of the group
 
Copy content magma:CompositionFactors(G);
 
Copy content gap:CompositionSeries(G);
 
Copy content sage:G.composition_series()
 
Copy content sage_gap:G.CompositionSeries()
 
Copy content oscar:composition_series(G)
 
Derived length:$0$
Copy content comment:Derived length of the group
 
Copy content magma:DerivedLength(G);
 
Copy content gap:DerivedLength(G);
 
Copy content sage:libgap(G).DerivedLength()
 
Copy content sage_gap:G.DerivedLength()
 
Copy content oscar:derived_length(G)
 

This group is nonabelian and perfect (hence nonsolvable). Whether it is almost simple has not been computed.

Copy content comment:Determine if the group G is abelian
 
Copy content magma:IsAbelian(G);
 
Copy content gap:IsAbelian(G);
 
Copy content sage:G.is_abelian()
 
Copy content sage_gap:G.IsAbelian()
 
Copy content oscar:is_abelian(G)
 
Copy content comment:Determine if the group G is cyclic
 
Copy content magma:IsCyclic(G);
 
Copy content gap:IsCyclic(G);
 
Copy content sage:G.is_cyclic()
 
Copy content sage_gap:G.IsCyclic()
 
Copy content oscar:is_cyclic(G)
 
Copy content comment:Determine if the group G is nilpotent
 
Copy content magma:IsNilpotent(G);
 
Copy content gap:IsNilpotentGroup(G);
 
Copy content sage:G.is_nilpotent()
 
Copy content sage_gap:G.IsNilpotentGroup()
 
Copy content oscar:is_nilpotent(G)
 
Copy content comment:Determine if the group G is solvable
 
Copy content magma:IsSolvable(G);
 
Copy content gap:IsSolvableGroup(G);
 
Copy content sage:G.is_solvable()
 
Copy content sage_gap:G.IsSolvableGroup()
 
Copy content oscar:is_solvable(G)
 
Copy content comment:Determine if the group G is supersolvable
 
Copy content gap:IsSupersolvableGroup(G);
 
Copy content sage:G.is_supersolvable()
 
Copy content sage_gap:G.IsSupersolvableGroup()
 
Copy content oscar:is_supersolvable(G)
 
Copy content comment:Determine if the group G is simple
 
Copy content magma:IsSimple(G);
 
Copy content gap:IsSimpleGroup(G);
 
Copy content sage:G.is_simple()
 
Copy content sage_gap:G.IsSimpleGroup()
 
Copy content oscar:is_simple(G)
 

Group statistics

Copy content comment:Compute statistics for the group G
 
Copy content magma:// Magma code to output the first two rows of the group statistics table element_orders := [Order(g) : g in G]; orders := Set(element_orders); printf "Orders: %o\n", orders; printf "Elements: %o %o\n", [#[x : x in element_orders | x eq n] : n in orders], Order(G); cc_orders := [cc[1] : cc in ConjugacyClasses(G)]; printf "Conjugacy classes: %o %o\n", [#[x : x in cc_orders | x eq n] : n in orders], #cc_orders;
 
Copy content gap:# Gap code to output the first two rows of the group statistics table element_orders := List(Elements(G), g -> Order(g)); orders := Set(element_orders); Print("Orders: ", orders, "\n"); element_counts := List(orders, n -> Length(Filtered(element_orders, x -> x = n))); Print("Elements: ", element_counts, " ", Size(G), "\n"); cc_orders := List(ConjugacyClasses(G), cc -> Order(Representative(cc))); cc_counts := List(orders, n -> Length(Filtered(cc_orders, x -> x = n))); Print("Conjugacy classes: ", cc_counts, " ", Length(ConjugacyClasses(G)), "\n");
 
Copy content sage:# Sage code to output the first two rows of the group statistics table element_orders = [g.order() for g in G] orders = sorted(list(set(element_orders))) print("Orders:", orders) print("Elements:", [element_orders.count(n) for n in orders], G.order()) cc_orders = [cc[0].order() for cc in G.conjugacy_classes()] print("Conjugacy classes:", [cc_orders.count(n) for n in orders], len(cc_orders))
 
Copy content sage_gap:# Sage code (using the GAP interface) to output the first two rows of the group statistics table element_orders = [g.Order() for g in G.Elements()] orders = sorted(list(set(element_orders))) print("Orders:", orders) print("Elements:", [element_orders.count(n) for n in orders], G.Order()) cc_orders = [cc.Representative().Order() for cc in G.ConjugacyClasses()] print("Conjugacy classes:", [cc_orders.count(n) for n in orders], len(cc_orders))
 
Copy content oscar:# Oscar code to output the first two rows of the group statistics table element_orders = [order(g) for g in elements(G)] orders = sort(unique(element_orders)) println("Orders: ", orders) element_counts = [count(==(n), element_orders) for n in orders] println("Elements: ", element_counts, " ", order(G)) ccs = conjugacy_classes(G) cc_orders = [order(representative(cc)) for cc in ccs] cc_counts = [count(==(n), cc_orders) for n in orders] println("Conjugacy classes: ", cc_counts, " ", length(ccs))
 

Order 1 2 3 4 5 6 7 8 9 10 12 14 15 17 20 21 30 42 63 85
Elements 1 1371135 53338112 1332495360 3428941824 9038929920 2005401600 2961100800 8021606400 8949104640 15792537600 6016204800 31444697088 11890851840 6317015040 4010803200 33690746880 12032409600 48129638400 47563407360 252680601600
Conjugacy classes   1 4 4 8 5 11 2 3 2 6 9 2 14 4 2 4 8 4 12 16 121
Divisions 1 4 3 8 3 7 1 3 1 3 5 1 5 1 1 1 2 1 1 1 53

Minimal presentations

Permutation degree:$256$
Transitive degree:not computed
Rank: $2$
Inequivalent generating pairs: not computed

Minimal degrees of faithful linear representations

Over $\mathbb{C}$ Over $\mathbb{R}$ Over $\mathbb{Q}$
Irreducible 255 not computed not computed
Arbitrary not computed not computed not computed

Constructions

Show commands: Gap / Magma / Oscar / SageMath


Groups of Lie type:$\ASL(4,4)$
Copy content magma:G := ASL(4,4);
 
Copy content gap:F = GF(4); al = F.0; MS = MatrixSpace(F, 4, 4) G = MatrixGroup([MS([[1, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [1, 0, 0, 0]]), MS([[al^1, 0, 0, 0], [0, 0, al^2, 0], [0, 0, 0, 0], [1, 0, 0, 0]]), MS([[1, 0, 0, 1], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0]])])
 
Copy content sage:F = GF(4); al = F.0; MS = MatrixSpace(F, 4, 4) G = MatrixGroup([MS([[1, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [1, 0, 0, 0]]), MS([[al^1, 0, 0, 0], [0, 0, al^2, 0], [0, 0, 0, 0], [1, 0, 0, 0]]), MS([[1, 0, 0, 1], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0]])])
 
Copy content oscar:F = GF(4); al = F.0; MS = MatrixSpace(F, 4, 4) G = MatrixGroup([MS([[1, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [1, 0, 0, 0]]), MS([[al^1, 0, 0, 0], [0, 0, al^2, 0], [0, 0, 0, 0], [1, 0, 0, 0]]), MS([[1, 0, 0, 1], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0]])])
 
Permutation group:Degree $256$ $\langle(1,2)(3,5)(4,11)(6,15)(7,17)(8,20)(9,12)(10,26)(13,31)(14,23)(16,36)(18,39) \!\cdots\! \rangle$ Copy content Toggle raw display
Copy content comment:Define the group as a permutation group
 
Copy content magma:G := PermutationGroup< 256 | (1,2)(3,5)(4,11)(6,15)(7,17)(8,20)(9,12)(10,26)(13,31)(14,23)(16,36)(18,39)(19,43)(21,46)(22,47)(24,27)(25,56)(28,63)(29,65)(30,68)(32,70)(33,44)(34,50)(35,74)(37,81)(38,51)(40,86)(41,89)(42,93)(45,96)(48,84)(49,98)(52,108)(53,111)(54,114)(55,117)(57,122)(58,78)(59,126)(60,128)(61,109)(62,125)(64,137)(66,139)(67,132)(69,145)(71,151)(72,153)(73,155)(75,158)(76,77)(79,152)(80,133)(82,165)(83,163)(85,105)(87,171)(88,176)(90,167)(91,94)(92,120)(95,185)(97,189)(99,100)(101,179)(102,194)(103,115)(104,146)(106,198)(107,129)(110,203)(112,207)(113,123)(116,188)(118,210)(119,136)(121,201)(124,217)(127,184)(130,215)(131,142)(134,221)(135,138)(140,232)(141,235)(143,219)(144,240)(147,154)(148,149)(150,229)(156,244)(157,192)(159,247)(160,178)(161,237)(162,238)(164,202)(166,241)(168,190)(169,172)(170,187)(173,195)(174,196)(175,206)(177,197)(180,208)(181,191)(182,183)(186,254)(193,256)(199,236)(200,252)(204,211)(205,255)(209,218)(212,213)(214,220)(216,248)(222,251)(223,239)(224,234)(225,226)(227,250)(228,243)(230,242)(231,233)(245,253)(246,249), (2,3,5)(4,9,12)(6,14,8)(7,17,19)(10,24,27)(13,29,31)(15,33,34)(18,39,41)(20,38,44)(22,47,49)(23,50,51)(25,55,57)(28,61,63)(30,66,68)(35,73,75)(36,76,77)(37,79,81)(40,84,87)(42,91,94)(45,72,97)(46,99,100)(48,104,105)(52,95,71)(53,110,112)(54,113,115)(56,119,120)(58,107,123)(59,124,127)(60,103,129)(62,131,133)(64,135,138)(67,141,125)(69,145,147)(70,148,149)(74,156,157)(78,114,128)(80,161,132)(82,164,166)(83,167,168)(85,169,171)(86,172,146)(88,175,177)(90,160,179)(92,182,117)(96,186,187)(101,191,190)(102,193,165)(106,197,196)(108,199,200)(111,205,180)(116,203,208)(118,209,211)(121,214,184)(122,183,136)(126,220,222)(130,224,218)(134,219,227)(140,229,233)(142,235,237)(143,238,239)(144,228,232)(150,243,242)(151,245,236)(153,170,246)(155,192,212)(158,213,244)(159,204,234)(162,221,225)(163,181,178)(173,194,241)(174,206,216)(176,198,248)(185,252,253)(188,255,207)(189,249,254)(195,202,256)(201,217,251)(210,247,215)(223,226,250)(230,240,231), (2,4,10,25,56,74,78,36,58,26,35,15,11,16,6)(3,7,18,40,85,170,190,99,178,89,97,50,43,21,8)(5,13,30,67,142,236,243,149,231,139,95,44,65,32,14)(9,22,48,86,173,218,124,204,110,202,151,129,109,52,23)(12,28,62,132,225,197,112,206,127,223,153,113,98,45,20)(17,37,80,131,224,205,175,208,164,247,156,179,93,75,38)(19,42,92,183,126,221,166,227,177,251,245,167,152,71,33)(24,53,84,165,250,186,168,94,184,161,210,244,150,70,54)(27,59,125,219,256,200,228,135,203,172,176,192,101,46,60)(29,64,136,182,111,194,238,193,209,255,246,232,154,72,34)(31,69,146,105,196,222,211,214,239,248,157,229,137,73,51)(39,82,141,234,217,253,233,147,216,122,188,96,128,76,83)(41,88,57,121,215,155,103,47,102,133,226,254,242,148,90)(49,106,120,213,163,81,162,171,187,230,138,220,237,185,107)(55,116,198,158,115,63,134,104,195,252,191,100,140,66,118)(61,130,119,212,240,145,241,235,199,181,91,180,169,189,123)(68,143,87,174,207,249,160,79,159,117,201,108,114,77,144) >;
 
Copy content gap:G := Group( (1,2)(3,5)(4,11)(6,15)(7,17)(8,20)(9,12)(10,26)(13,31)(14,23)(16,36)(18,39)(19,43)(21,46)(22,47)(24,27)(25,56)(28,63)(29,65)(30,68)(32,70)(33,44)(34,50)(35,74)(37,81)(38,51)(40,86)(41,89)(42,93)(45,96)(48,84)(49,98)(52,108)(53,111)(54,114)(55,117)(57,122)(58,78)(59,126)(60,128)(61,109)(62,125)(64,137)(66,139)(67,132)(69,145)(71,151)(72,153)(73,155)(75,158)(76,77)(79,152)(80,133)(82,165)(83,163)(85,105)(87,171)(88,176)(90,167)(91,94)(92,120)(95,185)(97,189)(99,100)(101,179)(102,194)(103,115)(104,146)(106,198)(107,129)(110,203)(112,207)(113,123)(116,188)(118,210)(119,136)(121,201)(124,217)(127,184)(130,215)(131,142)(134,221)(135,138)(140,232)(141,235)(143,219)(144,240)(147,154)(148,149)(150,229)(156,244)(157,192)(159,247)(160,178)(161,237)(162,238)(164,202)(166,241)(168,190)(169,172)(170,187)(173,195)(174,196)(175,206)(177,197)(180,208)(181,191)(182,183)(186,254)(193,256)(199,236)(200,252)(204,211)(205,255)(209,218)(212,213)(214,220)(216,248)(222,251)(223,239)(224,234)(225,226)(227,250)(228,243)(230,242)(231,233)(245,253)(246,249), (2,3,5)(4,9,12)(6,14,8)(7,17,19)(10,24,27)(13,29,31)(15,33,34)(18,39,41)(20,38,44)(22,47,49)(23,50,51)(25,55,57)(28,61,63)(30,66,68)(35,73,75)(36,76,77)(37,79,81)(40,84,87)(42,91,94)(45,72,97)(46,99,100)(48,104,105)(52,95,71)(53,110,112)(54,113,115)(56,119,120)(58,107,123)(59,124,127)(60,103,129)(62,131,133)(64,135,138)(67,141,125)(69,145,147)(70,148,149)(74,156,157)(78,114,128)(80,161,132)(82,164,166)(83,167,168)(85,169,171)(86,172,146)(88,175,177)(90,160,179)(92,182,117)(96,186,187)(101,191,190)(102,193,165)(106,197,196)(108,199,200)(111,205,180)(116,203,208)(118,209,211)(121,214,184)(122,183,136)(126,220,222)(130,224,218)(134,219,227)(140,229,233)(142,235,237)(143,238,239)(144,228,232)(150,243,242)(151,245,236)(153,170,246)(155,192,212)(158,213,244)(159,204,234)(162,221,225)(163,181,178)(173,194,241)(174,206,216)(176,198,248)(185,252,253)(188,255,207)(189,249,254)(195,202,256)(201,217,251)(210,247,215)(223,226,250)(230,240,231), (2,4,10,25,56,74,78,36,58,26,35,15,11,16,6)(3,7,18,40,85,170,190,99,178,89,97,50,43,21,8)(5,13,30,67,142,236,243,149,231,139,95,44,65,32,14)(9,22,48,86,173,218,124,204,110,202,151,129,109,52,23)(12,28,62,132,225,197,112,206,127,223,153,113,98,45,20)(17,37,80,131,224,205,175,208,164,247,156,179,93,75,38)(19,42,92,183,126,221,166,227,177,251,245,167,152,71,33)(24,53,84,165,250,186,168,94,184,161,210,244,150,70,54)(27,59,125,219,256,200,228,135,203,172,176,192,101,46,60)(29,64,136,182,111,194,238,193,209,255,246,232,154,72,34)(31,69,146,105,196,222,211,214,239,248,157,229,137,73,51)(39,82,141,234,217,253,233,147,216,122,188,96,128,76,83)(41,88,57,121,215,155,103,47,102,133,226,254,242,148,90)(49,106,120,213,163,81,162,171,187,230,138,220,237,185,107)(55,116,198,158,115,63,134,104,195,252,191,100,140,66,118)(61,130,119,212,240,145,241,235,199,181,91,180,169,189,123)(68,143,87,174,207,249,160,79,159,117,201,108,114,77,144) );
 
Copy content sage:G = PermutationGroup(['(1,2)(3,5)(4,11)(6,15)(7,17)(8,20)(9,12)(10,26)(13,31)(14,23)(16,36)(18,39)(19,43)(21,46)(22,47)(24,27)(25,56)(28,63)(29,65)(30,68)(32,70)(33,44)(34,50)(35,74)(37,81)(38,51)(40,86)(41,89)(42,93)(45,96)(48,84)(49,98)(52,108)(53,111)(54,114)(55,117)(57,122)(58,78)(59,126)(60,128)(61,109)(62,125)(64,137)(66,139)(67,132)(69,145)(71,151)(72,153)(73,155)(75,158)(76,77)(79,152)(80,133)(82,165)(83,163)(85,105)(87,171)(88,176)(90,167)(91,94)(92,120)(95,185)(97,189)(99,100)(101,179)(102,194)(103,115)(104,146)(106,198)(107,129)(110,203)(112,207)(113,123)(116,188)(118,210)(119,136)(121,201)(124,217)(127,184)(130,215)(131,142)(134,221)(135,138)(140,232)(141,235)(143,219)(144,240)(147,154)(148,149)(150,229)(156,244)(157,192)(159,247)(160,178)(161,237)(162,238)(164,202)(166,241)(168,190)(169,172)(170,187)(173,195)(174,196)(175,206)(177,197)(180,208)(181,191)(182,183)(186,254)(193,256)(199,236)(200,252)(204,211)(205,255)(209,218)(212,213)(214,220)(216,248)(222,251)(223,239)(224,234)(225,226)(227,250)(228,243)(230,242)(231,233)(245,253)(246,249)', '(2,3,5)(4,9,12)(6,14,8)(7,17,19)(10,24,27)(13,29,31)(15,33,34)(18,39,41)(20,38,44)(22,47,49)(23,50,51)(25,55,57)(28,61,63)(30,66,68)(35,73,75)(36,76,77)(37,79,81)(40,84,87)(42,91,94)(45,72,97)(46,99,100)(48,104,105)(52,95,71)(53,110,112)(54,113,115)(56,119,120)(58,107,123)(59,124,127)(60,103,129)(62,131,133)(64,135,138)(67,141,125)(69,145,147)(70,148,149)(74,156,157)(78,114,128)(80,161,132)(82,164,166)(83,167,168)(85,169,171)(86,172,146)(88,175,177)(90,160,179)(92,182,117)(96,186,187)(101,191,190)(102,193,165)(106,197,196)(108,199,200)(111,205,180)(116,203,208)(118,209,211)(121,214,184)(122,183,136)(126,220,222)(130,224,218)(134,219,227)(140,229,233)(142,235,237)(143,238,239)(144,228,232)(150,243,242)(151,245,236)(153,170,246)(155,192,212)(158,213,244)(159,204,234)(162,221,225)(163,181,178)(173,194,241)(174,206,216)(176,198,248)(185,252,253)(188,255,207)(189,249,254)(195,202,256)(201,217,251)(210,247,215)(223,226,250)(230,240,231)', '(2,4,10,25,56,74,78,36,58,26,35,15,11,16,6)(3,7,18,40,85,170,190,99,178,89,97,50,43,21,8)(5,13,30,67,142,236,243,149,231,139,95,44,65,32,14)(9,22,48,86,173,218,124,204,110,202,151,129,109,52,23)(12,28,62,132,225,197,112,206,127,223,153,113,98,45,20)(17,37,80,131,224,205,175,208,164,247,156,179,93,75,38)(19,42,92,183,126,221,166,227,177,251,245,167,152,71,33)(24,53,84,165,250,186,168,94,184,161,210,244,150,70,54)(27,59,125,219,256,200,228,135,203,172,176,192,101,46,60)(29,64,136,182,111,194,238,193,209,255,246,232,154,72,34)(31,69,146,105,196,222,211,214,239,248,157,229,137,73,51)(39,82,141,234,217,253,233,147,216,122,188,96,128,76,83)(41,88,57,121,215,155,103,47,102,133,226,254,242,148,90)(49,106,120,213,163,81,162,171,187,230,138,220,237,185,107)(55,116,198,158,115,63,134,104,195,252,191,100,140,66,118)(61,130,119,212,240,145,241,235,199,181,91,180,169,189,123)(68,143,87,174,207,249,160,79,159,117,201,108,114,77,144)'])
 
Copy content sage_gap:G = gap.new('Group( (1,2)(3,5)(4,11)(6,15)(7,17)(8,20)(9,12)(10,26)(13,31)(14,23)(16,36)(18,39)(19,43)(21,46)(22,47)(24,27)(25,56)(28,63)(29,65)(30,68)(32,70)(33,44)(34,50)(35,74)(37,81)(38,51)(40,86)(41,89)(42,93)(45,96)(48,84)(49,98)(52,108)(53,111)(54,114)(55,117)(57,122)(58,78)(59,126)(60,128)(61,109)(62,125)(64,137)(66,139)(67,132)(69,145)(71,151)(72,153)(73,155)(75,158)(76,77)(79,152)(80,133)(82,165)(83,163)(85,105)(87,171)(88,176)(90,167)(91,94)(92,120)(95,185)(97,189)(99,100)(101,179)(102,194)(103,115)(104,146)(106,198)(107,129)(110,203)(112,207)(113,123)(116,188)(118,210)(119,136)(121,201)(124,217)(127,184)(130,215)(131,142)(134,221)(135,138)(140,232)(141,235)(143,219)(144,240)(147,154)(148,149)(150,229)(156,244)(157,192)(159,247)(160,178)(161,237)(162,238)(164,202)(166,241)(168,190)(169,172)(170,187)(173,195)(174,196)(175,206)(177,197)(180,208)(181,191)(182,183)(186,254)(193,256)(199,236)(200,252)(204,211)(205,255)(209,218)(212,213)(214,220)(216,248)(222,251)(223,239)(224,234)(225,226)(227,250)(228,243)(230,242)(231,233)(245,253)(246,249), (2,3,5)(4,9,12)(6,14,8)(7,17,19)(10,24,27)(13,29,31)(15,33,34)(18,39,41)(20,38,44)(22,47,49)(23,50,51)(25,55,57)(28,61,63)(30,66,68)(35,73,75)(36,76,77)(37,79,81)(40,84,87)(42,91,94)(45,72,97)(46,99,100)(48,104,105)(52,95,71)(53,110,112)(54,113,115)(56,119,120)(58,107,123)(59,124,127)(60,103,129)(62,131,133)(64,135,138)(67,141,125)(69,145,147)(70,148,149)(74,156,157)(78,114,128)(80,161,132)(82,164,166)(83,167,168)(85,169,171)(86,172,146)(88,175,177)(90,160,179)(92,182,117)(96,186,187)(101,191,190)(102,193,165)(106,197,196)(108,199,200)(111,205,180)(116,203,208)(118,209,211)(121,214,184)(122,183,136)(126,220,222)(130,224,218)(134,219,227)(140,229,233)(142,235,237)(143,238,239)(144,228,232)(150,243,242)(151,245,236)(153,170,246)(155,192,212)(158,213,244)(159,204,234)(162,221,225)(163,181,178)(173,194,241)(174,206,216)(176,198,248)(185,252,253)(188,255,207)(189,249,254)(195,202,256)(201,217,251)(210,247,215)(223,226,250)(230,240,231), (2,4,10,25,56,74,78,36,58,26,35,15,11,16,6)(3,7,18,40,85,170,190,99,178,89,97,50,43,21,8)(5,13,30,67,142,236,243,149,231,139,95,44,65,32,14)(9,22,48,86,173,218,124,204,110,202,151,129,109,52,23)(12,28,62,132,225,197,112,206,127,223,153,113,98,45,20)(17,37,80,131,224,205,175,208,164,247,156,179,93,75,38)(19,42,92,183,126,221,166,227,177,251,245,167,152,71,33)(24,53,84,165,250,186,168,94,184,161,210,244,150,70,54)(27,59,125,219,256,200,228,135,203,172,176,192,101,46,60)(29,64,136,182,111,194,238,193,209,255,246,232,154,72,34)(31,69,146,105,196,222,211,214,239,248,157,229,137,73,51)(39,82,141,234,217,253,233,147,216,122,188,96,128,76,83)(41,88,57,121,215,155,103,47,102,133,226,254,242,148,90)(49,106,120,213,163,81,162,171,187,230,138,220,237,185,107)(55,116,198,158,115,63,134,104,195,252,191,100,140,66,118)(61,130,119,212,240,145,241,235,199,181,91,180,169,189,123)(68,143,87,174,207,249,160,79,159,117,201,108,114,77,144) )')
 
Copy content oscar:G = @permutation_group(256, (1,2)(3,5)(4,11)(6,15)(7,17)(8,20)(9,12)(10,26)(13,31)(14,23)(16,36)(18,39)(19,43)(21,46)(22,47)(24,27)(25,56)(28,63)(29,65)(30,68)(32,70)(33,44)(34,50)(35,74)(37,81)(38,51)(40,86)(41,89)(42,93)(45,96)(48,84)(49,98)(52,108)(53,111)(54,114)(55,117)(57,122)(58,78)(59,126)(60,128)(61,109)(62,125)(64,137)(66,139)(67,132)(69,145)(71,151)(72,153)(73,155)(75,158)(76,77)(79,152)(80,133)(82,165)(83,163)(85,105)(87,171)(88,176)(90,167)(91,94)(92,120)(95,185)(97,189)(99,100)(101,179)(102,194)(103,115)(104,146)(106,198)(107,129)(110,203)(112,207)(113,123)(116,188)(118,210)(119,136)(121,201)(124,217)(127,184)(130,215)(131,142)(134,221)(135,138)(140,232)(141,235)(143,219)(144,240)(147,154)(148,149)(150,229)(156,244)(157,192)(159,247)(160,178)(161,237)(162,238)(164,202)(166,241)(168,190)(169,172)(170,187)(173,195)(174,196)(175,206)(177,197)(180,208)(181,191)(182,183)(186,254)(193,256)(199,236)(200,252)(204,211)(205,255)(209,218)(212,213)(214,220)(216,248)(222,251)(223,239)(224,234)(225,226)(227,250)(228,243)(230,242)(231,233)(245,253)(246,249), (2,3,5)(4,9,12)(6,14,8)(7,17,19)(10,24,27)(13,29,31)(15,33,34)(18,39,41)(20,38,44)(22,47,49)(23,50,51)(25,55,57)(28,61,63)(30,66,68)(35,73,75)(36,76,77)(37,79,81)(40,84,87)(42,91,94)(45,72,97)(46,99,100)(48,104,105)(52,95,71)(53,110,112)(54,113,115)(56,119,120)(58,107,123)(59,124,127)(60,103,129)(62,131,133)(64,135,138)(67,141,125)(69,145,147)(70,148,149)(74,156,157)(78,114,128)(80,161,132)(82,164,166)(83,167,168)(85,169,171)(86,172,146)(88,175,177)(90,160,179)(92,182,117)(96,186,187)(101,191,190)(102,193,165)(106,197,196)(108,199,200)(111,205,180)(116,203,208)(118,209,211)(121,214,184)(122,183,136)(126,220,222)(130,224,218)(134,219,227)(140,229,233)(142,235,237)(143,238,239)(144,228,232)(150,243,242)(151,245,236)(153,170,246)(155,192,212)(158,213,244)(159,204,234)(162,221,225)(163,181,178)(173,194,241)(174,206,216)(176,198,248)(185,252,253)(188,255,207)(189,249,254)(195,202,256)(201,217,251)(210,247,215)(223,226,250)(230,240,231), (2,4,10,25,56,74,78,36,58,26,35,15,11,16,6)(3,7,18,40,85,170,190,99,178,89,97,50,43,21,8)(5,13,30,67,142,236,243,149,231,139,95,44,65,32,14)(9,22,48,86,173,218,124,204,110,202,151,129,109,52,23)(12,28,62,132,225,197,112,206,127,223,153,113,98,45,20)(17,37,80,131,224,205,175,208,164,247,156,179,93,75,38)(19,42,92,183,126,221,166,227,177,251,245,167,152,71,33)(24,53,84,165,250,186,168,94,184,161,210,244,150,70,54)(27,59,125,219,256,200,228,135,203,172,176,192,101,46,60)(29,64,136,182,111,194,238,193,209,255,246,232,154,72,34)(31,69,146,105,196,222,211,214,239,248,157,229,137,73,51)(39,82,141,234,217,253,233,147,216,122,188,96,128,76,83)(41,88,57,121,215,155,103,47,102,133,226,254,242,148,90)(49,106,120,213,163,81,162,171,187,230,138,220,237,185,107)(55,116,198,158,115,63,134,104,195,252,191,100,140,66,118)(61,130,119,212,240,145,241,235,199,181,91,180,169,189,123)(68,143,87,174,207,249,160,79,159,117,201,108,114,77,144))
 
Direct product: not computed
Semidirect product: not computed
Trans. wreath product: not isomorphic to a non-trivial transitive wreath product

Elements of the group are displayed as matrices in $\ASL(4,4)$.

Homology

Abelianization: $C_1 $
Copy content comment:The abelianization of the group
 
Copy content magma:quo< G | CommutatorSubgroup(G) >;
 
Copy content gap:FactorGroup(G, DerivedSubgroup(G));
 
Copy content sage:G.quotient(G.commutator())
 
Copy content sage_gap:G.FactorGroup(G.DerivedSubgroup())
 
Copy content oscar:quo(G, derived_subgroup(G)[1])
 
Schur multiplier: not computed
Copy content comment:The Schur multiplier of the group
 
Copy content gap:AbelianInvariantsMultiplier(G);
 
Copy content sage:G.homology(2)
 
Copy content sage_gap:G.AbelianInvariantsMultiplier()
 
Commutator length: $1$
Copy content comment:The commutator length of the group
 
Copy content gap:CommutatorLength(G);
 
Copy content sage_gap:G.CommutatorLength()
 

Subgroups

Copy content comment:List of subgroups of the group
 
Copy content magma:Subgroups(G);
 
Copy content gap:AllSubgroups(G);
 
Copy content sage:G.subgroups()
 
Copy content sage_gap:G.AllSubgroups()
 
Copy content oscar:subgroups(G)
 

Subgroup data has not been computed.

Character theory

Copy content comment:Character table
 
Copy content magma:CharacterTable(G); // Output not guaranteed to exactly match the LMFDB table
 
Copy content gap:CharacterTable(G); # Output not guaranteed to exactly match the LMFDB table
 
Copy content sage:G.character_table() # Output not guaranteed to exactly match the LMFDB table
 
Copy content sage_gap:G.CharacterTable() # Output not guaranteed to exactly match the LMFDB table
 
Copy content oscar:character_table(G) # Output not guaranteed to exactly match the LMFDB table
 

Complex character table

The $121 \times 121$ character table is not available for this group.

Rational character table

The $53 \times 53$ rational character table is not available for this group.