↑

Properties

Label 598...000.a
Order \( 2^{40} \cdot 3^{21} \cdot 5^{10} \cdot 7^{6} \cdot 11^{4} \cdot 13^{3} \cdot 17^{2} \cdot 19^{2} \cdot 23 \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \)
Exponent \( 2^{5} \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19 \cdot 23 \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \)
Simple yes
$\card{G^{\mathrm{ab}}}$ \( 1 \)
$\card{Z(G)}$ 1
$\card{\Aut(G)}$ \( 2^{41} \cdot 3^{21} \cdot 5^{10} \cdot 7^{6} \cdot 11^{4} \cdot 13^{3} \cdot 17^{2} \cdot 19^{2} \cdot 23 \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \)
$\card{\mathrm{Out}(G)}$ \( 2 \)
Perm deg. $45$
Trans deg. not computed
Rank $2$

Related objects

Downloads

Learn more

Show commands: Gap / Magma / SageMath

Copy content magma:G := AlternatingGroup(45);
 
Copy content gap:G := AlternatingGroup(45);
 
Copy content sage:G = AlternatingGroup(45)
 
Copy content comment:Define the group as a permutation group
 

Group information

Description:$A_{45}$
Order: \(598\!\cdots\!000\)\(\medspace = 2^{40} \cdot 3^{21} \cdot 5^{10} \cdot 7^{6} \cdot 11^{4} \cdot 13^{3} \cdot 17^{2} \cdot 19^{2} \cdot 23 \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \)
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()
 
Exponent: \(9419588158802421600\)\(\medspace = 2^{5} \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19 \cdot 23 \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \)
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()
 
Automorphism group:Group of order \(119\!\cdots\!000\)\(\medspace = 2^{41} \cdot 3^{21} \cdot 5^{10} \cdot 7^{6} \cdot 11^{4} \cdot 13^{3} \cdot 17^{2} \cdot 19^{2} \cdot 23 \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \)
Copy content comment:Automorphism group
 
Copy content gap:AutomorphismGroup(G);
 
Copy content magma:AutomorphismGroup(G);
 
Copy content sage_gap:G.AutomorphismGroup()
 
Composition factors:$A_{45}$
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()
 
Derived length:$0$
Copy content comment:Derived length of the group
 
Copy content magma:DerivedLength(G);
 
Copy content gap:DerivedLength(G);
 
Copy content sage_gap:G.DerivedLength()
 

This group is nonabelian and simple (hence nonsolvable, perfect, quasisimple, and almost simple).

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 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 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 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 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 comment:Determine if the group G is simple
 
Copy content magma:IsSimple(G);
 
Copy content gap:IsSimpleGroup(G);
 
Copy content sage_gap:G.IsSimpleGroup()
 

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))
 

Order 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 48 50 51 52 54 55 56 57 58 60 62 63 65 66 68 69 70 72 74 75 76 77 78 80 82 84 85 87 88 90 91 92 93 95 96 99 100 102 104 105 108 110 111 112 114 115 116 117 119 120 123 124 126 130 132 133 135 136 138 140 143 144 145 148 150 152 153 154 155 156 160 161 165 168 170 171 174 175 176 180 182 184 185 186 187 189 190 195 198 200 203 204 207 208 209 210 216 217 220 221 222 224 225 228 230 231 232 234 238 240 247 248 252 253 255 259 260 261 264 266 270 272 273 275 276 279 280 285 286 288 290 297 299 300 304 306 308 310 312 315 319 322 323 325 330 336 340 341 342 345 348 350 351 352 357 360 364 368 372 374 377 378 380 385 390 391 396 399 400 403 406 408 414 418 420 425 429 432 434 435 437 440 442 450 455 456 459 460 462 465 468 475 476 480 483 494 495 504 506 510 520 522 525 528 532 540 546 550 552 555 558 560 561 570 572 580 585 594 595 598 600 609 612 616 620 624 627 630 638 644 646 650 651 660 663 665 672 680 684 690 693 696 700 702 714 715 720 728 741 744 748 756 759 760 765 770 780 782 792 798 805 812 816 819 825 828 836 840 855 858 868 870 880 884 897 900 910 912 920 924 930 935 936 945 952 957 966 969 975 988 990 1001 1008 1012 1015 1020 1023 1035 1040 1044 1045 1050 1064 1071 1080 1085 1092 1100 1104 1105 1122 1131 1140 1144 1155 1160 1170 1173 1188 1190 1196 1197 1218 1224 1232 1235 1254 1260 1265 1275 1287 1288 1292 1300 1302 1305 1309 1311 1320 1326 1330 1360 1365 1368 1380 1386 1395 1400 1428 1430 1449 1456 1463 1482 1485 1495 1496 1512 1518 1520 1530 1540 1547 1560 1575 1584 1595 1596 1610 1615 1638 1650 1656 1672 1680 1683 1710 1716 1729 1740 1755 1768 1771 1785 1794 1800 1820 1827 1848 1860 1870 1872 1881 1890 1904 1925 1932 1938 1950 1955 1976 1980 1989 1995 2002 2024 2030 2040 2070 2079 2090 2093 2100 2128 2142 2145 2184 2210 2223 2244 2261 2275 2277 2280 2288 2310 2340 2380 2394 2415 2431 2436 2448 2470 2475 2508 2520 2530 2574 2618 2640 2652 2660 2691 2717 2730 2760 2772 2805 2856 2860 2898 2907 2926 2964 2990 3003 3036 3045 3060 3080 3094 3120 3135 3150 3192 3220 3230 3276 3300 3315 3366 3420 3432 3458 3465 3542 3570 3588 3640 3696 3705 3740 3762 3780 3795 3864 3876 3927 3960 3978 3990 4004 4080 4095 4140 4180 4200 4284 4290 4368 4389 4420 4446 4485 4488 4560 4620 4641 4680 4760 4788 4830 4845 4862 4940 5005 5016 5040 5060 5148 5187 5236 5304 5313 5320 5355 5460 5544 5610 5712 5720 5796 5852 5928 5985 6006 6120 6160 6188 6270 6435 6440 6545 6552 6630 6732 6840 6864 6916 6930 7140 7245 7280 7293 7315 7410 7480 7524 7735 7854 7920 7956 7980 8008 8190 8360 8415 8568 8580 8645 8778 8840 9009 9240 9282 9360 9405 9576 9660 9945 10010 10296 10472 10710 10920 11088 11220 11781 11970 12012 12540 12870 13090 13260 13860 14280 15015 15708 15960 16380 17160 18018 18480 19635 20020 21420 21945 23205 24024 25740 27720 30030 32760 45045 60060
Elements 1 626788575285503108897974951935 72254745204101002097961368775155448380 11162352152740145645385936831945263599411200 232155055904428588255413921369924374803515624 308179964845731853561068104009914861291470312900 235380256901802865626901076106318817405986350400 17704603356388843260207038285846561104036941004800 29188114794088623352234297589017891863004036675200 212262978691973786638866913884745971675002421532440 340431641320338860456443140971960099149846790208000 4196889107695004645266751274913441735076864230502400 12603700001844666928985475406981646745677849472000 4295241489687908950480864852528506230349956116536000 7691674128751007217750937491587855705453697067989120 11642872841567399271198461802423720988598882795520000 5184755782749580830657856767938161543864320000 52799549263491946820927009449877383364038746191088000 32873362371246151167947272007987212960875970560000 67698195787780020234222091306037765333599670800588800 69712914170451918471483923223098255408856979864396800 123657405456825943300620985352767537376478830952384000 4627191064964458965864873984000000 186373197456921525062635063206143985487172369645568000 372184392944014738873126679809915566951628800000000 15313590275602429537498703793121301695713542904960000 35211536317033266359223299733046332048636641280000000 96114776626343491906653498686603613583239687573504000 197148859681517207177257101825146880000000 390079865819319125617083358947101128676309421906249600 44263098818818056837216433183968460800000000 85360533387754976899524979257914320684371148800000000 335439157965374366560160515737662525933510316294144000 1626846745935008083428598996011066972151550976000000 155431412546051924155699008381744212544866277338649600 766444229021177715282880837105658279264041808510976000 80184350108242301159617091307149369278464000000000 82150532569871479214314270959444617285733298176000000 346073611386597949494649172232286854959095254835200000 1023992691762665049717398772278224320321337588658995200 121567297627520522928824351113473287667056640000000000 1513769607258517505017627431898366226094201259512192000 1390956056575351099557711180182066454237020160000000000 6278170815670262028549111793922912893138596249600000 2670039507473377244229618635001410303500103345413324800 1430914025340517259361770142254362460160000000 168133177295015683147420634939548238116930191360000000 33387838065237400606902043904943444320894976000000000 736289392579415913769783581530063178704084336640000 46105207543831183890165230272303510697044172636160000 69108003923568151319898947027040415288275763200000000 155933313935531610911273173178670450033826209792000 77044262593668035056226598696521171116410619822080000 11505693792520899163735783028645486938287243264000000 4396958773029062669614463168874267200716800000000 790523958891760269217363273593689619397968414169497600 55960198101975372991189759466463518156390400000000 13494341245485615458252445551163619639400972820480000 1835027913573837321917453956093283926244534550528000 214684872813703498622277026548525064679681955430400000 75845060569432591966177092741375650751176245248000000 920851517410575973374987190686564089856000000000 102983741767563994681846427668267091113289637358464000 779042980639314784659181073459226680151361254850560000 25258070284096324865279383761752051322716160000000000 121633310956556804531161865353789994387295436800000000 151879876723912207083962752653765231234429222912000000 138202092281608684084836205798231463978573660160000 323679201083659910941472508281375325260232010014720000 70490591808253039913969422453122017976216170004480000 364701892882561568786473053340419863001169920000000000 571523649043215484155217905297443005526419214008320000 4199804779118256881194765393182821422419140935680000 234984060096898988398305718389478176011059200000000 16313834004866278105539263660345417980561588224000000 367461377449316655360503839946593406403417829158912000 36748323295371394983241912451885614024213463040000 93154104620993313067483705662443373912391680000000 1196330995312135721684826033226473519081062400000000 16585546883338009439581209244839228288037882429440000 615780171342363876327566098087215089672257536000000000 202944358820880189905563914301387517206006784655360000 43804242948310795006611274563854810040867225600000000 226969265826207568393510609285090144520551686144000000 26564492331749310071954987405421549388355862528000000 381555729863350033443518780591951201013099746935603200 268704636665484919701487726482068547562792550400000000 51212983159063460902074670127686019109497918447616000 98787119333354515028648256490408022951067648000000000 296102038095822036249800033261023426253502283776000000 794477955133477141461027890243392414914360115200000000 174741671611915625267214625616326544002646016000000 4531364322038905333927677221188846734645657600000000 2906843407839867750814946404199497715404701696000000 1354688712282748628829287086274066114386722816000000 1589353605209266042202004875446936036084351009554432000 972538381020164183430594808907786301336453120000000000 13829213801732821391932025118505616220880896000000000 246508174412821225515080528028178958901133474652160000 22362243375845037626678240660312296012094657495040000 337971534394239617739562028232509976111119739125760000 23694314669379128274448390636277008118655221760000000 190959084921201608816473888698656725521892638720000000 87890007586605841234551816867929036009106309120000000 3056617238978939792204982128465956495514664960000000 391150575919902986167750184719671044224402386026496000 808439808756483692467152439184082245910528000000 166102562515668340134147908225844676737430978560000000 5614473562536585272214348355342195888352133120000000 303096843409155898383352605141024615872593920000000000 134571736063995503259858530583779524906293657600000000 2604181584306072116305319872841691361789870080000000 13480688858228365110539089915654447501753712640000000 41617404848825826915929346432729829820698914816000000 3217777851906460402305752249796078022636339200000000 536654136757336887743600687202266957222564069376000000 232598762793989267203817258463778890402968371200000000 2528510671661143315001437345457727530462085120000000 100993703134681361215067955504570831462200454905856000 508806055079937745759528065388456388241820735242240000 385821033314501614980998107228130098571900289024000000 1203565118993512751036720343457398256026255360000000 45900944941807660743044848864055136098451456000000000 12114801559669331305643111342464130031078604800000000 67494284203412748340887247844136573918888591360000000 881939304364677611104184078719850084580406498689024000 56051361270389310882611490615950463702508167168000000 9616347941576655646116367506819278906484326400000000 107767766545477652758525370716808752310255616000000000 74914887530340428070865910772681327394160640000000000 18854826318576748662674339226952686452610170880000000 54367315066659817949933675501536267612245196800000000 323712840623308945647342571071770528355951181824000000 634289518456632340383920522120079506556200873164800000 172269877637109598512636197400302746515839311872000000 57589291184963045607294324055586978675451494400000000 21047053303151808000658179231517586252365824000000000 142235181561654394095781859982791085611278663680000000 12491595614674401896275599951585979950484684800000000 84729474592186313180818585357163250880138444800000000 1084005916646550021685673346350118592818708480000000 944436713673246145853252625546771081889774148087808000 109277905139182882763698159269760065431666688000000000 39484695461596033791299741514823746560458752000000000 98764160831463867455533692993547096849162331750400000 10409173413699704337657397204179479152212049920000000 404129124545541197844470140188032821163458560000000000 89004628620148954287174971350935799899095040000000000 39254937046980846875680301337572661376371916800000000 302516527442277450251902686999637960607567708160000000 21045340484479218333310041469322214122418339840000000 111586024332362375736636004426450811158792151040000000 59438723250927060276837538338958275564797952000000000 339535806462319047107002675390701710296290754560000000 149173619593792734671896661014643696803009658880000000 392758395033892690155801611060508522835492208640000000 18626941975232793776628171106634685006584217600000000 80391277463360345807770941865361367650795520000000000 576697935931457967488110727718174212897984741376000000 21491607401156077615097557284852379695867494400000000 12555617814475917003672839756699630225389765263360000 461861856623475654679394445929180367043952640000000000 76292937886302878377273403973404266607665049763840000 31918901298260314640917920760335597205192704000000000 435687175894641341722069469390815888949070790656000000 5816279024191617411553815234507358517715271680000000 165326097661926682588427509284363248312569036800000000 14675098679679461569615254535596560645672140800000000 25786429793308607079573631979442627604448477184000000 3626114499339401841329350684667754810703872000000000 82960713151469383183944372917932605803436441600000000 75031858965802989420586212407670609807409152000000000 291406433907093413337392728636092784575081527377920000 19415904146591710702231052311637564455883636736000000 5431978955802203742248213874506705567540183040000000 207677466780347560003408266485516866431221760000000000 22721756340844922697909840387405564548952883200000000 28049943565137852260200597031810070271229952000000000 1102497567448890800039328271410080514048000000000 208368850939536343336584596194229172160797081600000000 37475633103220612331442093200394021010145280000000000 241542160357177723622665239107960463059260538880000000 111865247899679266388124082415570351960332959744000000 108930180962853268569529626227564653166827929600000000 248751510805859267663596775147824724307785809920000000 448660624847995254269098199992907172460593574379520000 3124927399829681153656299934578310215892992000000000 4545442297638695893834287784840107326334566400000000 1020578243551759595082845675391994036224000000000 36879866628246335930275577872592885291522457600000000 516558924868459308251523513931223739769499740569600000 261828040574438130791553433434029961341797662720000000 151968859886153350450319423570490924875227594752000000 58466383609716615132924321356626449200578560000000000 62024564927784073023196404184355709185084620800000000 59493122186054047623905173985321855540527104000000000 228797594491233480446009939125368554325540864000000000 52568064451299880395193778383474000017122918400000000 59640708408715196718927502170199715487940608000000000 169917927365738912730061308942695617989181440000000000 81319047709525466305289311410198493153992376320000000 267491201096357758137066165511559864407662463549440000 194813187521839472736026677419027168476457861120000000 54176730464438493913932591257091356460318720000000000 276010052624203853940013567071074028934397952000000000 15144382562384313790029994486749732763729920000000000 52883386766348450292645075815940634422804480000000000 117471982059768024586961886790957329549361152000000000 61445030643360589759730210194610558989749977088000000 632226695213498124688012031125002728712728739840000 397843862421367386950398546046303599721517570785280000 2549493198326517360655651353274887362838528000000000 123539191994188903938071919305558908248556830720000000 53083008969729051230670927768963539458436628480000000 149527776081850243202453951869572143830479667200000000 296829332172407430674846554579795819018321920000000000 149466393579353588751221417406571498451238912000000000 322750940709160599846727901968882372462950481920000000 96133240079077551088879263037839454242865152000000000 74798775896677445465773555381915781397322137600000000 1470720799411999171535057446066298324436454334791680000 46910674849207919436063984900257927476228915200000000 1308717048465245340042902494052957209543311360000000 138451644520231706668938844323677910954147840000000000 11484468209051477972538705980765909664399360000000000 287095057880926446851783318189277793580010700800000000 45622509864790310664364287374392721229742080000000000 67608943414873027092793141274581956488148811776000000 135321493489265406206659832696863485172541030400000000 167032019710479537545598362901922851143968358400000000 1345678024115880787103229795162367373346692136960000 168581060267556165858322392175847408589078528000000000 260614860273377330200355471668099597090160640000000000 143018545501205772561298754725102481198882488320000000 304026180654331214139613446060574176384126640128000000 37992322238239926389153971044518927823116697600000000 100281267716968424360916066158485533550329200640000000 251836254453642514867290866306647821188176281600000000 130857033966021148207063606730483455672618844160000000 290748453492486584004771573079723613003710464000000000 249382334029755895101607231526061733678625587200000000 21186811806040855440229459742031876194304000000000 11362970298126993857701877693887445102759525744640000 220666060203442147226990503432002417757582786560000000 216941453158465830607738731224283570241536000000000 304798980742592917365534697522870460154167033856000000 55901704583852321668081572075699172430391017472000000 28645167831772077241849416066967843645685760000000000 14694397328275385557006083012629806399566643200000000 86634999922878901131429835942330363872804864000000000 22236322739726630980371478075792098740246937600000000 100476336308968152839744189880611969663867289600000000 141014370846627451540842507285833739620099358720000000 12460648006820853600204495989131011985873305600000000 62981643537274485473313346608662729472344064000000000 215535533090955305517050741433617504620511232000000000 53594184975573563871847294576907578433863680000000000 87171158946880869977671169671090193999251636224000000 3244572356320602201877795749123751038418944000000000 50479378991169362096223388814305382525947084800000000 34676953109194328485464687004823403897531924480000000 71326467901112472332205046006749930677757542400000000 12184091133351344911953767407106783060889698304000000 25173026276405764848897971695214165628026880000000000 470666445782296510201029698511593582109917184000000 1458604281734882528452031303075536520085504000000000 146824672545979052738917526813728908426136780800000000 9366515195785790336223777317135517128589312000000000 58819456902125276784911588855648543341490995200000000 28867513456775718864519600540839149495186882560000000 136665171687712587873210601171114325006352384000000000 146385911923151589621435208686806830020349132800000000 8745740693362419747604391498737044719193292800000000 217882869034912241577672004483872973117963587747840000 46873910997445217304844499018674653238394880000000000 21991125228771793041670181269719943842103296000000000 1350225016218977944294604828543608109924352000000000 7668091081120525292433535993311391991306649600000000 38281560696838259908462353269219698881331200000000000 577079859213520607396819536291032442370271467274240000 69691914079324244926080819821820909925171200000000 1306852942306711068859739049126057486833418240000000 178009257240297908574349942701871599798190080000000000 56609269816801332356541874556655909454353530880000000 84225716486561650286948445460291488479340134400000000 78644368022782412905714400339912881976943575040000000 23799345240647411318528651072912873201553899520000000 114580671327088308967397664267871374582743040000000000 65100528362166092278619407616684470783338086400000000 42600506006225140513519644407285511062814720000000000 52482749159754942499962547889063933456429875200000000 1953622250968584016416934328135998630995689472000000 161008151406090621761967479590967544846420541440000000 25317396169756081667749159680659598347882987520000000 379071545195326255551066092308354051552051200000000 160782554926720691615541883730722735301591040000000000 43938775780419827175296875118798849635988275200000000 132518002612221776383127179566948857627541504000000000 1682110606772248572460004216279580115206144000000000 15239680708415488519870366430776729215613009920000000 22623077586136384145223724261706932499628687360000000 53987556250210102214482704742964502170748125184000000 360191564800360203922562077266813952410398490624000000 38242397974897760409834770299123310442577920000000000 57111683277187091760981910212374961716283310080000000 69866452278812143821904436618393935405252608000000000 2883569787690374471608005501549963755000954880000000 30691251248327225616267231500322689620377600000000000 87802387449244981484167379145324030924423168000000000 28719256730320305711244515045863324831349473280000000 35913517487672224517761106285172209629318348800000000 96228192682074086809032650185214647427137536000000000 72728122062544362159468040341614836102201344000000000 473692734993572871134954951204941389812534618357760000 28872096811485464224881819602987317132410224640000000 109278780324568729079703741726313318341319065600000000 68906809254308867835232235884595457986396160000000000 179748428144369784692605085820223218876678144000000000 52216920583605184117388499139620698336148848640000000 1119456574148178149698756762173241458425856000000000 6359205969045202134626845469493344405028864000000000 58149690698497316800954314615944722600742092800000000 128224539132888036164490980432847822619027832832000000 52465886344508857264018930480551629414203392000000000 30261573730850644457639490259318171965692313600000000 275715671911856707526168899604132025633386004480000000 80391277463360345807770941865361367650795520000000000 6244372319163123027223857860209903534205829120000000 69382683763666913771108863876135845100309708800000000 26899176649645017295679546897171708413948723200000000 15185308275877921749525891697006163482430668800000000 62498547996593623073125998691566204317859840000000000 69462563925268941046442152920119423658885120000000000 5886695308806549344437853855661021600940032000000000 25560303603735084308111786644371306637688832000000000 2450329856749040037055829170794993681432576000000000 171993338318850569103185891642153778442384048128000000 5909747477041007251546721961684199487098060800000000 77262353710127571323304672581270253388116787200000000 5417673046443849391393259125709135646031872000000000 4910600199732356098602757040051630339260416000000000 170162122269360273469427430689464595526262456320000000 116932767219433230265848642713252898401157120000000000 9313237951267760144252221639909514134369075200000000 29130631726161572274959147318505711374381875200000000 57290335663544154483698832133935687291371520000000000 858564230783127445980521423093538779320811520000000 154505442349125240275551515082161516343354982400000000 16952023320732630822810727278048604940402688000000000 4679794270422359530006349293317746908043673600000000 110761315616185365335151075458942328763318272000000000 55125447403447094268185788707676366389116928000000000 161869218997526486159206107173170576350731304960000000 22655723648765188364008174525692749065224192000000000 108353460928876987827865182514182712920637440000000000 811945358523410118596963698762667895375790080000000 110635869153832793539558659358749003969095270400000000 105766773532696900585290151631881268845608960000000000 225132335903099201717292650149599571920908451840000000 82316466533937464596085482274431113189811814400000000 137506980256058194306724178035441724328598568960000000 51561302097189739035328948920542118562234368000000000 141630696093256508299761111742880149248674365440000000 50989863966530347213113027065497747256770560000000000 50346052552811529697795943390428331256053760000000000 26456916341768956637224836597621054252247941120000000 20837204024784036120743304329650521715507200000000000 9975904476002158900318867785864146505537945600000000 61382502496654451232534463000645379240755200000000000 41002241223813717612250866431711056402317312000000000 64199779258670212529604418969631229210525696000000000 1616737248619709749939777482299049752553062400000000 8652241996711050989927063657929774894940160000000000 301297813431980942484227284410256781180284698624000000 9587639573100630438102010089133743082674585600000000 93821349698415838872127969800515854952457830400000000 6957385841886161485605456457353415132761292800000000 52628823879740251230677374364031603418595328000000000 19288928803128256347065783264908687284633600000000000 46008546486723151754601215959868351947839897600000000 22968936418102955945077411961531819328798720000000000 45832268530835323586959065707148549833097216000000000 1087935082199885401397800395363092406258892800000000 91245019729580621328728574748785442459484160000000000 237628740229613245301380098622008056311493689344000000 8182437001414523334365413142567072185712640000000000 37747263283171981706900662486046413982867128320000000 32251088958830444612293989618927325139907379200000000 28270609647086603285119425814739456022272802816000000 66987694172006844542452741595704312555634688000000000 174556565608318217255866778354296650652345958400000000 123514525205586091200984501727351127258549452800000000 85750695960917702194955671323052125494181888000000000 28481481158447665371895990832299455967710412800000000 107229120612078499433001193182562284183591321600000000 96567165880389586115190524227407134884453416960000000 9287439508189456099531301358358518250340352000000000 36775538858435172320854713437309737101164544000000000 5842386307920919054485101218091730223497216000000000 16643158212739054347551589147276126745264128000000000 40276842042249223758236754712342665004843008000000000 3333952643965445779318928692744083474481152000000000 7948541700302072388212951986955229188849664000000000 39557612720066201905411098378193688844042240000000000 24215356798499023794863809728548409326960640000000000 65582357930636071580023663100689536767754240000000000 85055314851195972337875797390670719937014661120000000 79061769720457033825157673821314680240268640256000000 5525152662241955123924824228874079713624064000000000 129980067486048809519303547494249163447682990080000000 28481481158447665371895990832299455967710412800000000 62572951029922901195832101070960925989666816000000000 74998257595912347687751198429879445181431808000000000 93265364793271978771906947716064702468037017600000000 45418159039354270731180155670528253832567193600000000 3086228608500521015530525322385389965541376000000000 110975818856151062625998325428559560955317452800000000 45311447297530376728016349051385498130448384000000000 36117820309625662609288394171394237640212480000000000 4769626031318987024001720952777420855836672000000000 173400633626948858600365607463594038584965857280000000 2173553319244279275818711421582567662419968000000000 69560240236071676159788193618523027122893619200000000 66278479705928159905871683606466266545310924800000000 96091366931334903413954085129215438487552000000000 60154852446721362207883773740632471655940096000000000 68160809609960224821631431051656817700503552000000000 4510641812423838407313844701947877641945088000000000 2814375608542259424100394351017732803133440000000000 55388731240747371808303872410141870299734343680000000 41674408049568072241486608659301043431014400000000000 33228394684855609600545322637682698628995481600000000 41064327942392965442450215072230618251007098880000000 65474669329764747981370093867355071190138880000000000 103846819915720096294252424178854466621643161600000000 32156510985344138323108376746144547060318208000000000 8279730937814658737721824986411697071718400000000000 25560303603735084308111786644371306637688832000000000 7154439046978480536002581429166131283755008000000000 7911522544013240381082219675638737768808448000000000 20942265557682106891099993259043717623316480000000000 31070706718306544042068353635235770146593177600000000 75904752523721233801107672830041223231176704000000000 38577857606256512694131566529817374569267200000000000 15336182162241050584867071986622783982613299200000000 61187836759836416655735632478597296708124672000000000 20179187055580329716930357877135242082385920000000000 88752124723322215069694386114846760672459489280000000 6765962718635757610970767052921816462917632000000000 84080103906196573680425389015817580956897771520000000 31549027972597412804847559158696785387873894400000000 29550943889693723953054140685686194432901120000000000 14731800599197068295808271120154891017781248000000000 62788273246279720254450919295704023068395438080000000 44244329879291436696378282859957941109260288000000000 57538345774641748226052506731918092864061440000000000 6369438095990563921635631522354847434565222400000000 28576736948275249537019388794949286924124160000000000 24921296013641707200408991978262023971746611200000000 28106724827415459248581569900295515757608960000000000 48849704258432593083034582490403314545459200000000000 21032833786828898524568447554815835599682928640000000 81256597556317132299489694851254074766838988800000000 6023586253674334206433696779059561601014169600000000 20179187055580329716930357877135242082385920000000000 33383346296178863573249673597907441287168000000000000 26453388072861608704547359906160485418926080000000000 52581195984826459148115675382706687940388454400000000 26267505679727754624937013942832172829245440000000000 71507324923575811909277123669177758145052672000000000 17427479729819375664621672712071345434787840000000000 142542443654075868467273455460919859615468879872000000 96771547457931783668095532726027269756535439360000000 13637867879623005817167926727928983026757795840000000 30683174603261876346368213807822604702056448000000000 56818818634934012906621125488313982551641292800000000 2050291732919926548779020319067217109975040000000000 24553000998661780493013785200258151696302080000000000 24432643150629124706283325468884337227202560000000000 24971743981280658024701317872954862076952576000000000 48332210450699068509884105654811198005811609600000000 34623951931056350248308789138680536583110656000000000 72585803092107239261319401780570852609690173440000000 5910188777938744790610828137137238886580224000000000 28202952687765730707256055170204744286208000000000000 22980963379017069569513894117973352255586304000000000 63172308798408752739853481349418406123667456000000000 32743918342039715845685687465992000660045824000000000 14430349437186556022148744101985054875870822400000000 44452701919539277057585715903254446326415360000000000 22013658606087632418469481320511173180784640000000000 103231853834653648599245196567287125585066721280000000 43341384371550795131146073005673085168254976000000000 36134756883439650067612472358494219331541401600000000 22418918569647739175536982121557097600516096000000000 29362108965430091533361690284290196421738496000000000 25266082333018659511218291189024289971524075520000000 5159688615660808944184056310199176805744640000000000 41149714780006946873740337631805199540551680000000000 638789200623078619285944770461261721763840000000000 17656788673632788502314063142493336822087680000000000 10001857931896337337956786078232250423443456000000000 42274707258125490335393044165811772519245414400000000 34476101204642677945229830799967226838384640000000000 39284801597858848788822056320413042714083328000000000 42530250970059412078008902976907949873351884800000000 19391756161954709531805785632133138181720637440000000 604103814163906929550961344010876469903360000000000 25276300230360250038021655681656069897270067200000000 41044019985911113734584121468768239576363827200000000 9493827052815888457298663610766485322570137600000000 31108245441701184217720219031623370218143744000000000 22444645478124518907200644949366419104989184000000000 9258685825501563046591575967156169896624128000000000 24860211742168070173886098695624451528694169600000000 18124578919012150691206539620554199252179353600000000 38815385416540374527276386366391683581267148800000000 9439884853652161818336739385705312110510080000000000 17925844501040526231873134580855140049852825600000000 16135402694295068778375581765627431530528768000000000 4324111511910070653627933830814694731939840000000000 8029358766147448121593773776373643796262420480000000 8443126825626778272301183053053198409400320000000000 51145966427252869247795934484961952860523724800000000 16669763219827228896594643463720417372405760000000000 10915800065374019125425959632504228053233172480000000 28889044441018044421830529421650542458830848000000000 6188284030377967779858643082321474238598348800000000 5286335518045210618268574055994974781885644800000000 3974688359432489186668100793981184046530560000000000 15823045088026480762164439351277475537616896000000000 10507002271891101849974805577132869131698176000000000 30958131693964853665104337861195060834467840000000000 15431143042502605077652626611926949827706880000000000 2957503207183966610498777306808675081388032000000000 41327516210404921514906234340478627679746129920000000 3758868177019865339428203918289898034954240000000000 47124617208434755440324637435125100626051072000000000 3984905866792882751885006626085021077733376000000000 29319171780754949647539990562661204672643072000000000 11958458646669856647710010471641479153157406720000000 10835346092887698782786518251418271292063744000000000 17289894363531327962006238453818150602407936000000000 14240740579223832685947995416149727983855206400000000 19895152279798001546544993596091531742150656000000000 30860720187302734964257529666523631834261094400000000 13693019787715223736488457130913199984476160000000000 2498375540214707488762806213359601400676352000000000 16351076570036414226512687044561056452050944000000000 6726395685193443238976785959045080694128640000000000 26671621151723566234551429541952667795849216000000000 13326896263979522567063632073936911214837760000000000 13116471586127214316004732620137907353550848000000000 99173931853100105373070098500001875719901675520000000 2362717139841058213354871034353650193399808000000000 25491838504796508189429344358716740637766451200000000 18813135225984426023838160611040939664945971200000000 10930392988439345263337277183448256127959040000000000 20638754462643235776736225240796707222978560000000000 24689828868004168124244202579083119724331008000000000 6150875198759779646337060957201651329925120000000000 9080634175011148372618661044710858937073664000000000 953242305856673560068289754957704393339699200000000 23848130156594935120008604763887104279183360000000000 28481481158447665371895990832299455967710412800000000 11820377555877489581221656274274477773160448000000000 4937785923448823104976140601753547873189888000000000 7687309354506792273116326810337235079004160000000000 2379802904282057601261362870345877002649600000000000 22553209062119192036569223509739388209725440000000000 22515004868338075392803154808141862425067520000000000 14990253241288244932576837280157608404058112000000000 4268233170803781785424189102319386258466406400000000 78580207795027385329366873522299896528413655040000000 21210843314022510534670918497268466599329792000000000 23344279955737463696639795516179489477990809600000000 10471132778841053445549996629521858811658240000000000 5199198119396113739945465692434618054711705600000000 10319377231321617888368112620398353611489280000000000 7665470407476943431431337245535140661166080000000000 10089593527790164858465178938567621041192960000000000 5496426188472356475278173669391123081487974400000000 17613544092014159248342595710603475256606720000000000 19546114520503299765026660375107469781762048000000000 12946127799294393350861814014681570894413824000000000 7249245769966883154611536128130517638840320000000000 15898753437729956746672403175924736186122240000000000 2224078365519806037199337279445295512630067200000000 9287439508189456099531301358358518250340352000000000 1979996016362671924249453908127769666204467200000000 15290538762948666505745443796186406649331712000000000 15035472708079461357712815673159592139816960000000000 6663448131989761283531816036968455607418880000000000 8744314390751476210669821746758604902367232000000000 8713739864909687832310836356035672717393920000000000 8648223023820141307255867661629389463879680000000000 34405597559065588374240172938174452913615667200000000 28573449837880872507978599268304780230288998400000000 16511003570114588621388980192637365778382848000000000 8215811872629134241893074278547919990685696000000000 16402333863359412390232162552537736879800320000000000 2725500589325135442286697687301383346192384000000000 12107512233348197830158214726281145249431552000000000 7996137758387713540238179244362146728902656000000000 7949376718864978373336201587962368093061120000000000 2577509607099336232750768401113072938254336000000000 5076912862468389549357574123404537605652480000000000 7551907882921729454669391508564249688408064000000000 7517736354039730678856407836579796069908480000000000 24858836625136339513189921822928033936729702400000000 2489639961402767952088810387438763633541120000000000 18384509186410987297632954705052270169633587200000000 7154439046978480536002581429166131283755008000000000 7107678007455745369100603772766352647913472000000000 6980755185894035630366664419681239207772160000000000 19794481870901192454626108365610347748602675200000000 13837156838112226091609388258607023142207488000000000 10220627209969257908575116327380187548221440000000000 6765962718635757610970767052921816462917632000000000 2323663963975916755282889694942846057971712000000000 24873632800624022815717767927546595789661798400000000 9665661026622510872815381504174023518453760000000000 6390075900933771077027946661092826659422208000000000 12719002750183965397337922540739788948897792000000000 6245938850536768721907015533399003501690880000000000 12383252677585941466041735144478024333787136000000000 12028378166463569086170252538527673711853568000000000 9348598055067393660093483004832557443946905600000000 5809159909939791888207224237357115144929280000000000 5711526970276938243027270888830104806359040000000000 6980755185894035630366664419681239207772160000000000 17404625098427662424426571727826867895612211200000000 5394219916372663896192422506117321206005760000000000 11105746886649602139219693394947426012364800000000000 10153825724936779098715148246809075211304960000000000 2498375540214707488762806213359601400676352000000000 13527043790288372539682536438417282408906752000000000 9539252062637974048003441905554841711673344000000000 5809159909939791888207224237357115144929280000000000 2284610788110775297210908355532041922543616000000000 9021283624847676814627689403895755283890176000000000 10695967491321796411307260626415488334194278400000000 9773057260251649882513330187553734890881024000000000 1176585403981456261801971131248837924592025600000000 7615369293702584324036361185106806408478720000000000 7495126620644122466288418640078804202029056000000000 8307098671213902400136330659420674657248870400000000 8132823873915708643490113932299961202900992000000000 1659759974268511968059206924959175755694080000000000 6473063899647196675430907007340785447206912000000000 3046147717481033729614544474042722563391488000000000 4232387934384705518550977658645898177019904000000000 2792302074357614252146665767872495683108864000000000 5451001178650270884573395374602766692384768000000000 5155019214198672465501536802226145876508672000000000 4979279922805535904177620774877527267082240000000000 2323663963975916755282889694942846057971712000000000 4315375933098131116953938004893856964804608000000000 2489639961402767952088810387438763633541120000000000 1825735971695363164865127617455093331263488000000000 2655615958829619148894731079934681209110528000000000 995855984561107180835524154975505453416448000000000 59811110432740097280981580747828857532191866880000000000
Conjugacy classes   1 11 15 60 9 281 6 110 35 112 4 1264 3 60 111 70 2 394 2 391 62 26 1 1254 5 20 12 190 1 1398 1 10 29 12 26 959 1 9 21 386 1 656 1 75 116 5 417 16 12 54 29 12 197 10 4 3522 3 63 10 244 30 7 227 659 2 19 23 8 167 147 1 1587 7 5 80 884 6 15 4 6 19 30 25 88 56 182 40 93 2 75 63 4 8 20 5 2157 2 6 425 64 554 4 16 30 37 465 3 160 3 2 54 22 13 49 2 367 7 3 75 997 33 9 16 5 29 1362 35 13 1 10 3 7 25 55 148 15 2 177 7 20 2 1369 15 2 174 2 2 3 9 127 15 41 5 97 18 471 2 3 619 2 32 2 118 3 338 12 22 10 30 2 63 2 312 25 14 2 5 3 1 56 7 44 86 4 217 108 1 7 1 2 468 215 57 1 31 15 15 9 2 1 19 649 58 3 9 7 1 9 40 17 306 1 207 13 2 2 3 94 13 5 2052 1 12 1 1 7 1 115 4 9 13 63 2 20 220 4 129 2 27 5 9 3 44 301 2 138 74 2 9 68 20 15 142 3 25 2 1 74 7 91 22 5 33 2 7 2 18 3 53 58 3 41 6 470 1 10 2 1 2 659 5 6 2 33 33 39 26 4 8 1 62 7 98 37 4 2 10 7 3 22 17 77 405 1 94 43 4 2 15 18 5 11 7 889 12 47 1 7 24 6 3 7 51 8 9 292 2 4 57 4 16 1 18 3 2 4 148 5 44 3 1 157 2 5 14 1 3 12 11 9 4 1 180 2 2 3 20 2 98 13 58 1 87 1 1 23 2 7 2 20 12 2 13 460 2 2 8 4 2 1 1 1 2 2 268 13 15 5 39 12 31 66 2 2 70 17 3 7 2 8 1 1 5 1 5 3 31 90 2 156 3 12 2 42 5 1 40 2 3 3 115 3 18 55 1 3 2 3 1 20 2 1 54 2 118 1 7 6 3 1 2 1 12 2 1 2 2 132 3 15 7 1 1 53 5 2 4 1 6 1 14 17 68 4 3 20 1 2 1 29 2 198 76 22 6 7 1 1 1 3 2 11 163 1 11 3 29 11 13 2 1 115 7 59 7 23 17 1 2 2 6 1 9 3 2 23 40 2 15 6 1 12 4 1 32 1 6 4 11 19 1 20 1 39 1 24 12 3 6 1 1 2 3 1 4 44 1 21 8 3 13 2 4 1 9 32 6 2 4 1 2 6 1 168 2 23 8 5 4 2 1 2 3 3 13 1 8 2 3 3 2 4 5 92 19 10 1 7 1 2 1 3 13 6 4 2 4 4 1 2 10 4 2 2 1 1 30 24 2 2 2 1 2 2 1 1 3 2 1 12 3 15 1 3 2 22 2 2 1 2 47 2 1 2 1 2 2 5 2 1 3 24 1 5 2 1 10 2 3 1 2 18 5 4 2 2 9 5 1 2 1 3 1 2 2 2 1 4 2 1 2 1 44669
Divisions 1 11 15 60 9 281 6 110 35 112 4 1264 3 60 111 70 2 394 2 391 62 26 1 1254 5 20 12 190 1 1398 1 10 28 12 26 959 1 9 21 386 1 656 1 75 115 5 417 16 12 54 29 12 197 10 4 3522 3 63 10 244 30 7 227 659 2 18 23 8 167 147 1 1587 7 5 80 884 6 15 4 6 19 29 25 88 56 180 40 93 2 75 63 4 8 20 5 2157 1 6 425 64 554 4 14 30 37 465 3 160 3 2 54 22 13 49 2 367 7 3 75 997 33 9 16 5 29 1362 35 13 1 10 3 7 25 54 148 15 2 177 7 20 2 1369 15 2 174 2 2 3 9 127 15 41 5 97 18 471 2 3 619 2 32 1 118 3 338 12 22 10 29 2 63 2 312 25 14 2 5 3 1 56 7 44 86 4 217 105 1 7 1 2 468 215 57 1 31 15 15 9 2 1 18 649 58 3 9 7 1 9 40 17 306 1 207 13 2 1 3 94 13 5 2052 1 12 1 1 6 1 115 4 9 13 63 1 20 220 4 129 1 27 5 8 3 44 301 2 138 74 2 9 68 20 15 142 3 25 1 1 74 7 91 22 5 32 2 7 2 18 3 53 58 3 41 6 470 1 10 2 1 2 659 5 6 2 33 33 39 25 4 8 1 62 7 98 37 4 2 10 7 3 22 16 77 405 1 94 43 4 2 15 18 4 11 7 889 12 47 1 7 24 6 3 7 51 8 9 292 2 4 57 4 16 1 18 3 2 4 148 5 44 3 1 157 1 5 14 1 3 12 11 9 4 1 180 2 2 3 20 1 98 13 56 1 87 1 1 23 2 7 2 20 12 2 13 460 2 1 8 4 2 1 1 1 2 1 268 13 15 5 39 12 31 66 1 2 70 17 3 7 2 8 1 1 5 1 5 3 31 90 2 156 2 12 1 42 5 1 40 2 3 3 115 3 18 55 1 3 1 3 1 19 2 1 54 1 118 1 7 6 3 1 2 1 12 2 1 1 2 132 3 13 7 1 1 53 5 1 4 1 6 1 14 16 68 4 2 20 1 1 1 29 2 198 76 22 6 6 1 1 1 3 1 11 163 1 11 3 29 11 13 1 1 115 7 59 7 23 17 1 1 2 6 1 8 3 1 23 40 2 15 5 1 12 4 1 32 1 5 4 11 19 1 19 1 39 1 24 12 3 6 1 1 2 3 1 4 44 1 21 8 3 12 2 4 1 9 32 6 2 4 1 1 6 1 168 2 23 8 5 4 1 1 2 3 3 13 1 8 2 3 3 1 4 5 92 19 10 1 7 1 2 1 3 13 6 4 2 4 4 1 2 10 4 2 2 1 1 30 24 1 2 1 1 2 2 1 1 3 2 1 12 3 15 1 2 2 22 1 2 1 2 47 2 1 1 1 2 1 5 2 1 3 24 1 5 1 1 10 2 3 1 2 18 5 4 2 2 9 5 1 2 1 3 1 1 1 2 1 4 2 1 1 1 44601
Autjugacy classes 1 11 15 60 9 281 6 110 35 112 4 1264 3 60 111 70 2 394 2 391 62 26 1 1254 5 20 12 190 1 1398 1 10 28 12 26 959 1 9 21 386 1 656 1 75 115 5 417 16 12 54 29 12 197 10 4 3522 3 63 10 244 30 7 227 659 2 18 23 8 167 147 1 1587 7 5 80 884 6 15 4 6 19 29 25 88 56 180 40 93 2 75 63 4 8 20 5 2157 1 6 425 64 554 4 14 30 37 465 3 160 3 2 54 22 13 49 2 367 7 3 75 997 33 9 16 5 29 1362 35 13 1 10 3 7 25 54 148 15 2 177 7 20 2 1369 15 2 174 2 2 3 9 127 15 41 5 97 18 471 2 3 619 2 32 1 118 3 338 12 22 10 29 2 63 2 312 25 14 2 5 3 1 56 7 44 86 4 217 105 1 7 1 2 468 215 57 1 31 15 15 9 2 1 18 649 58 3 9 7 1 9 40 17 306 1 207 13 2 1 3 94 13 5 2052 1 12 1 1 6 1 115 4 9 13 63 1 20 220 4 129 1 27 5 8 3 44 301 2 138 74 2 9 68 20 15 142 3 25 1 1 74 7 91 22 5 32 2 7 2 18 3 53 58 3 41 6 470 1 10 2 1 2 659 5 6 2 33 33 39 25 4 8 1 62 7 98 37 4 2 10 7 3 22 16 77 405 1 94 43 4 2 15 18 4 11 7 889 12 47 1 7 24 6 3 7 51 8 9 292 2 4 57 4 16 1 18 3 2 4 148 5 44 3 1 157 1 5 14 1 3 12 11 9 4 1 180 2 2 3 20 1 98 13 56 1 87 1 1 23 2 7 2 20 12 2 13 460 2 1 8 4 2 1 1 1 2 1 268 13 15 5 39 12 31 66 1 2 70 17 3 7 2 8 1 1 5 1 5 3 31 90 2 156 2 12 1 42 5 1 40 2 3 3 115 3 18 55 1 3 1 3 1 19 2 1 54 1 118 1 7 6 3 1 2 1 12 2 1 1 2 132 3 13 7 1 1 53 5 1 4 1 6 1 14 16 68 4 2 20 1 1 1 29 2 198 76 22 6 6 1 1 1 3 1 11 163 1 11 3 29 11 13 1 1 115 7 59 7 23 17 1 1 2 6 1 8 3 1 23 40 2 15 5 1 12 4 1 32 1 5 4 11 19 1 19 1 39 1 24 12 3 6 1 1 2 3 1 4 44 1 21 8 3 12 2 4 1 9 32 6 2 4 1 1 6 1 168 2 23 8 5 4 1 1 2 3 3 13 1 8 2 3 3 1 4 5 92 19 10 1 7 1 2 1 3 13 6 4 2 4 4 1 2 10 4 2 2 1 1 30 24 1 2 1 1 2 2 1 1 3 2 1 12 3 15 1 2 2 22 1 2 1 2 47 2 1 1 1 2 1 5 2 1 3 24 1 5 1 1 10 2 3 1 2 18 5 4 2 2 9 5 1 2 1 3 1 1 1 2 1 4 2 1 1 1 44601

Minimal presentations

Permutation degree:$45$
Transitive degree:not computed
Rank: $2$
Inequivalent generating pairs: not computed

Minimal degrees of linear representations for this group have not been computed

Constructions

Show commands: Gap / Magma / SageMath


Permutation group:Degree $45$ $\langle(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45), (1,2,3)\rangle$ Copy content Toggle raw display
Copy content comment:Define the group as a permutation group
 
Copy content magma:G := PermutationGroup< 45 | (3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45), (1,2,3) >;
 
Copy content gap:G := Group( (3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45), (1,2,3) );
 
Copy content sage:G = PermutationGroup(['(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45)', '(1,2,3)'])
 
Transitive group: 45T10922 more information
Direct product: not isomorphic to a non-trivial direct product
Semidirect product: not isomorphic to a non-trivial semidirect product
Trans. wreath product: not isomorphic to a non-trivial transitive wreath product

Elements of the group are displayed as permutations of degree 45.

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())
 
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: not computed
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()
 

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
 

Complex character table

The $44669 \times 44669$ character table is not available for this group.

Rational character table

The $44601 \times 44601$ rational character table is not available for this group.