↑

Properties

Label 275...000.a
Order \( 2^{41} \cdot 3^{21} \cdot 5^{10} \cdot 7^{6} \cdot 11^{4} \cdot 13^{3} \cdot 17^{2} \cdot 19^{2} \cdot 23^{2} \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \)
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
$\card{\Aut(G)}$ \( 2^{42} \cdot 3^{21} \cdot 5^{10} \cdot 7^{6} \cdot 11^{4} \cdot 13^{3} \cdot 17^{2} \cdot 19^{2} \cdot 23^{2} \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \)
$\card{\mathrm{Out}(G)}$ \( 2 \)
Perm deg. $46$
Trans deg. not computed
Rank $2$

Related objects

Downloads

Learn more

Show commands: Gap / Magma / SageMath

Copy content magma:G := AlternatingGroup(46);
 
Copy content gap:G := AlternatingGroup(46);
 
Copy content sage:G = AlternatingGroup(46)
 
Copy content comment:Define the group as a permutation group
 

Group information

Description:$A_{46}$
Order: \(275\!\cdots\!000\)\(\medspace = 2^{41} \cdot 3^{21} \cdot 5^{10} \cdot 7^{6} \cdot 11^{4} \cdot 13^{3} \cdot 17^{2} \cdot 19^{2} \cdot 23^{2} \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \)
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 \(550\!\cdots\!000\)\(\medspace = 2^{42} \cdot 3^{21} \cdot 5^{10} \cdot 7^{6} \cdot 11^{4} \cdot 13^{3} \cdot 17^{2} \cdot 19^{2} \cdot 23^{2} \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \)
Copy content comment:Automorphism group
 
Copy content gap:AutomorphismGroup(G);
 
Copy content magma:AutomorphismGroup(G);
 
Copy content sage_gap:G.AutomorphismGroup()
 
Composition factors:$A_{46}$
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 99 100 102 104 105 108 110 111 112 114 115 116 117 119 120 123 124 126 129 130 132 133 135 136 138 140 143 144 145 148 150 152 153 154 155 156 160 161 165 168 170 171 174 175 176 180 182 184 185 186 187 189 190 195 198 200 203 204 205 207 208 209 210 216 217 220 221 222 224 225 228 230 231 232 234 238 240 247 248 252 253 255 259 260 261 264 266 270 272 273 275 276 279 280 285 286 288 290 297 299 300 304 306 308 310 312 315 319 322 323 325 330 333 336 340 341 342 345 348 350 351 352 357 360 364 368 370 372 374 377 378 380 385 390 391 396 399 400 403 406 408 414 418 420 425 429 432 434 435 437 440 442 444 450 455 456 459 460 462 465 468 475 476 480 483 493 494 495 504 506 510 513 520 522 525 528 532 540 546 550 552 555 558 560 561 570 572 580 585 594 595 598 600 609 612 616 620 624 627 630 638 644 646 650 651 660 663 665 672 680 682 684 690 693 696 700 702 714 715 720 728 741 744 748 754 756 759 760 765 770 780 782 792 798 805 812 816 819 825 828 836 840 850 855 858 868 870 874 880 884 897 900 910 912 920 924 930 935 936 945 952 957 966 969 975 988 990 1001 1008 1012 1015 1020 1023 1035 1040 1044 1045 1050 1064 1071 1080 1085 1092 1100 1104 1105 1116 1120 1122 1131 1140 1144 1155 1160 1170 1173 1188 1190 1196 1197 1200 1218 1224 1232 1235 1240 1254 1260 1265 1275 1276 1287 1288 1292 1300 1302 1305 1309 1311 1320 1326 1330 1360 1365 1368 1380 1386 1395 1400 1404 1428 1430 1449 1456 1463 1482 1485 1495 1496 1512 1518 1520 1530 1540 1547 1560 1564 1575 1584 1595 1596 1610 1615 1624 1638 1650 1656 1672 1680 1683 1710 1716 1729 1740 1755 1768 1771 1785 1794 1800 1820 1827 1840 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 2200 2210 2223 2244 2261 2275 2277 2280 2288 2310 2340 2380 2392 2394 2415 2431 2436 2448 2470 2475 2508 2520 2530 2574 2584 2618 2640 2652 2660 2691 2717 2730 2736 2760 2772 2805 2856 2860 2898 2907 2926 2964 2990 2992 3003 3036 3045 3060 3080 3094 3120 3135 3150 3192 3220 3230 3255 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 5775 5796 5852 5928 5985 6006 6120 6160 6188 6270 6279 6435 6440 6545 6552 6630 6732 6783 6840 6864 6916 6930 7140 7245 7280 7293 7315 7410 7480 7524 7590 7735 7854 7920 7956 7980 8008 8151 8190 8360 8415 8568 8580 8645 8778 8840 8855 9009 9240 9282 9360 9405 9576 9660 9945 10010 10296 10374 10472 10710 10920 11088 11115 11220 11781 11970 12012 12155 12540 12870 13090 13167 13260 13860 13923 14280 14630 14820 15015 15470 15708 15960 16380 16830 17160 17556 18018 18480 18564 19635 20020 21420 21840 21945 22440 23205 23940 24024 25740 26180 27720 30030 32760 36036 40040 45045 60060
Elements 1 4529527526065787881948393670655 959174580162263327431022346648848821520 210658263003655737628664894392199066017167360 8249430963647951570338592669024750982581640624 7463188410902829355762747563639615984287482729200 2706753340714171137613258698246946283124426921600 463461508337165255532109376702741178536525876428800 1079821468504496845808685065689927745933874132345600 7106227925040974504240889229512039800479869824688720 7829927141780669259183435790628582759950737869644800 144849202523871916475571252273213229405718791885209600 82824314297823955464740869335342957133086507264000 110147647665856318781423880517942588955029528935868800 325210098787386048915148068334389401013290483407428480 292525906637457322146711003664436454795217081466880000 19874897167206726517469922233424936331591680000 1814866980858397942288745182247529408955346290582560000 189021833634665369215633646076734770728612986880000 3169328777072751210128751089413379129233668638782832640 2397155485899063451770810748406535061825849641705388800 3360150015570900485666119176479643804976373397012864000 5200966124586095415746783142810699138122326867968000000 7868335494540564451803809454648781216491097445892096000 15081371018233177679339391127966387030268313600000000 415696352842579424080034967731234754983723287330560000 1452433283701911163755887832153028210593088143360000000 4114041072556065618241657679901266200424243343777792000 533461620314693619420813334350397440000000 13131230641673443382871762616337351235485703437861020800 135740169711042040967463728430836613120000000 4573571268324922817431095010449626640130297036800000000 7710424686960107032011792463818931331990574626057472000 27047489183034989059108803713184723237116124119040000 4123938975682340194231003544616731051441685533423078400 29002989061165672667173611036232211208608603217494016000 409831122775460650371376244458763442978816000000000 1668495725533964821809543768881086226020527955968000000 9855119881105689666974453659086737509520182373326848000 24115165385270291802903092156086271852240983064523571200 1118419138173188810945184030243954246536921088000000000 35943871827397439950016424217823403983074279036235040000 21327992867488716859884904762791685631634309120000000000 62673432711585049884664856886472017821374060621824000000 122590540494784400508505347720060733441949825950967654400 15460101669706078266157509457784216616960000000 7664762951737533878014854009296496880255446433136640000 1313937721702077548520346390150153271877441945600000000 15434878739173039788943092716393952552536664637440000 747260180256116084754970456039134997052858806763520000 1785097846741832519483971448280174128902538526720000000 2365082745783532705440928501737960116123288130355200 2359166817849534687360533491600554451952763288944640000 232875160081895619686144337551761176705750220800000000 54062801035659613483070768548072709160960000000000 33746153617329097068287231823828759448647991230514790400 734285769351033365403290201627968504489574400000000 567255433860708275658453279883806168365221796880384000 43016061045549399582737676638852243113611000692736000 6404788295394201279186740270460058176072280630874880000 2079008438389646689747686388991115198951777632256000000 14857553429931062665429469313991348678557696000000 5249283675923148439545069857237490904410322491614131200 24900072384514030443441335354475401916841403885813760000 542206575431934440441330771418944035060973568000000000 4636396128017018019355589804212130580536780390400000000 6748179417993359556030150318517618150063414444032000000 2227970724406126311321561685030918644670952325120000 13275263476640658551813169944232500105523500371599360000 3714264443692742980716274329033714302921714297733120000 16776287072597832164177760453659313698053816320000000000 55895404959481178444672250428974343192726293331902464000 95614881795989788192196809712436040611242663608320000 4096220686822611978256492498140261349588992000000000 651737824713690884274801325466226436536330029629440000 14665930355146739323251981916233245996197056188317440000 59925444694923900983780702820870336264789217443840000 2095791606033331771002253800471577037226639360000000 22854451565497105610275406913181657106428723200000000 254435324977150845663890948541290359336736910213120000 17852790149596099877710977710283013927414530048000000000 6996144805113335211641881215859248663570748626370560000 1152531106606004748311632273178047810188292915200000000 6301482921892116614460330634009238298203846123520000000 1099380374732590058606978620954483440330309894144000000 14320145439108269500708321371108477324167082636194611200 10520307942939713499039835216767225792520047820800000000 1162813075710246980704433001443297213032018343387136000 2363905916168857031342098178038147539101810688000000000 7731876275563564811635400353858442545694880301056000000 21082705951944333899498365153032970096944270065664000000 2666183865747331120009134200595169284725932032000000 95950539297235657032012056083992415470983577600000000 67906396423380342129009511885563119043601907712000000 16954529612086832173359979454948977415400849408000000 87016690127259421309513940656055654315363434342907904000 22368382763463776218903680604879084930738421760000000000 367109533315818679672179394975908795688943616000000000 9601026792539061058805772920161253963442700762767360000 42655985734977433719769809525583371263268618240000000000 2836811051263616763533428908500211719334441067069440000 12691418364693879169053976302346450959051518285905920000 1088961213357956707960601351040242105312216875008000000 6519806954139437410072611281798549497728089456640000000 4016063979484956245646570219542873303156785152000000000 97704829211387470021513424629551173400617287680000000 16686935046983569630558592107786991463207969622622208000 53006705268241738208451572268626222424340168704000000 6571463504080749813845017748579304845774432501760000000 127250099067849943877571584855034491904259522560000000 7745808220456206292019011020270629072299622400000000000 4689365275238787008525897720107874719655657472000000000 18180291377303578711623136962419629692643946004480000000 573049143956485421859162542016161866338398896128000000 993644462086064463865976288307574123873060878336000000 266265694024160879537313966503912316915815546880000000 25345000177198115747466507883929719117063738228736000000 10153648032986592705080920731714756052488762163200000000 58132199238724003929989935275450277432362270720000000 3268530284044204199177250683143978120578765297942528000 22145425886853027493131710370081459602134285764526080000 11108622233730831716332295982158731323278660541480960000 94901813445822987683469381947569719374968258560000000 1192622522732926381111471827721256895926973235200000000 358213612518012377089623971210423021934634598400000000 2176959280991991417005423693619763277516148572160000000 55138028072777850076300247823115818116743076270505984000 1287487120796778688793000007560407807494194110464000000 312834633579711114465666097525425741203138150400000000 1239329315272993006723041763243300651567939584000000000 2683311437302582071521251290559253414192087040000000000 865729706165769037584008334399285064840233615360000000 2028599788767004067554504171523452554841581158400000000 14691020675949469907141975644261063439589399724032000000 15034216541294864049282018842502150528487501645873152000 7556545778241510101188345750263710421925976580096000000 1766990611583878370991192054131635482252646809600000000 322704054382186697338754448307355892366861926400000000 21103756349349815702444215374944310602630079971328000000 26842059316156531462684416725854901916886106112000000000 266684461377061912616594591400583235513194905600000000 3736774349770718775659275977048466667272163819520000000 9972854430379875159348784740374133434619002880000000 33428640248003050880352536204150164130976160615464960000 5026783636402412607130115326408963009856667648000000000 1811893611753281154510314939055932076409749504000000000 4834618857345873379202594660859775981513039282176000000 159607325671572004181038052143017484768530923520000000 15491616440912412584038022040541258144599244800000000000 13920323916191296450514165519286359104218464256000000000 1304186021886579598873062897965819190881707622400000000 13557395380707065038571621469241342487460855152640000000 495623072122771047487455448683398274663752663040000000 3726035957166795882597208899225441625099449243402240000 2357701920896497471841648723854789016637407232000000000 9911193475031676605659213929856177000811664359424000000 2960442565767985970828985363660207444130605957120000000 27211236271121089477656287359457839453316475896463360000 856839327538646465533603815648846367127135846400000000 1479199505325830362862985330322649164774637568000000000 37597796832703964343646297147743527246589942693888000000 988613440988372498751534283952977418109793075200000000 370155305777153539657726557227564267854342976962560000 10622822702339940057626072256371148442010910720000000000 12521168281282342945208837583689893298962728726036480000 644720884556527252779053643050111966625398784000000000 28172996675945360511539558449765666794519423614976000000 133042630837199496335322014964119130634726932480000000 7169080544975087862345273299340312245527935713280000000 461951121863144580868017534807536323703655628800000000 20714558291557980145353218412080077561653801517056000000 433545441834240714367865424422218254929362944000000000 2530334280097760145210141875639843288138750361600000000 2218799257988745544294477995483973747161956352000000000 13709152452056763312889412393025160308296062976655360000 1003495434864475504399518815592974300157522739200000000 83289598455963189696150547920235616682417192960000000 9553163471895987760156780258333775855836200960000000000 2455939500933851533168384087348738558997299200000000000 566572898549675464563410777225855970670804992000000000 5071488810264897680180910048486370364620800000000 9585737775793915928297999470480072491943958937600000000 762976130253347059207174764157651605528772608000000000 11269361126938612924939104260239246342150198394880000000 2424257266311090495146724939125051096301379780608000000 1975347672737202630406611659868371072126130585600000000 9398597913260392712041763341244715903663772532736000000 11698599758247765861091370596489993404745694734319616000 23957776732027555511364966165100378321846272000000000 1290603546936279220826156747283396913893684019200000000 4694659920338094137381090106803172566630400000000 564791422843960595051027228459733122026360012800000000 24416788857968748693491688052018667780476712168325120000 16524390870306573422973890176577342020905861120000000000 11191427417455091660902984639156033186155158568960000000 3946797332961478105723086188589575156267555487744000000 672363411511741074028629695601204165806653440000000000 2377858028555266023893109979260186621078169190400000000 2101916726904065940841396838415473105390014562304000000 9902191201370020153692885941006889998352384000000000000 2900094560667608234411993544353190838820614963200000000 1763660948657720817259713278461620158000529408000000000 7816224658823989985582820211363998427502346240000000000 2905188674429640420309902406433737156995265331200000000 11495096801323168261361843672409413967886499960586240000 7698848222961648179601133790505149733522422366208000000 996851840545668288016359679130480958869864448000000000 3717987945818979020169125289729901954703818752000000000 10737892705328250041523893509008860603549220864000000000 395689998917129508280804795063526967297048576000000000 608158947813007178365418371883317295862251520000000000 5454888836205914779715372400910825244212592640000000000 2713325724543484546181978463334727893068407635968000000 14320869755354913769775297876701918766634749924474880000 15507349346401439247170404572061329806375913618800640000 19546114520503299765026660375107469781762048000000000 6698661060310884591183717729798591567595474255872000000 1569492182141702939056719601902049021248342589440000000 4585518466510074124875254524000212410801376460800000000 6827074639965370905521470755335303837421404160000000000 6816629206424304566791673006993337106984599552000000000 14574661751134205131878741622409884989157476925440000000 4023907501086250903781910748754636303789929267200000000 1246634868439248262945910395881980346997722316800000000 64342385270237850828727382531298258843998861484097536000 539472760765891073514735826352966165976632524800000000 12856379142192604907437276809932213900535398400000000000 6368775647930658506771186838889183903890800640000000000 198107076606137995026292678168211941710888960000000000 6649915087452063875447211041711522536539291648000000000 524658863445088572640189304805516294142033920000000000 2599812075740038394815777962353156327819620971970560000 6224712242063463611910305985945389147117007667200000000 6196646576364965033615208816216503257839697920000000000 8949267066708277105318298077717676453520841113600000000 44929330503127951704506614186589686628079800156160000 7419306226742884771580305254683363665305717964800000000 5994141786287678594608175848366290733073694720000000000 6392472730728927508615784494091184922293845360640000000 12281719587143052192035502786372668453135740452864000000 12728942198211272498202959477443156622166510796800000000 3882353882902833631253692581382631104550928384000000000 5792233852433777841947689925052899887328054476800000000 5970839888947059460868630162861174789963104911360000000 11463796166275185312188136310000531027003441152000000000 5737047376855734225961711205583251155104615628800000000 11161505395156367038235913648682058606413086720000000000 323073856248651343665735210522983712109363200000000 506325332205825139954816204587038321726573972029440000 9549247560053617384354215550717242901045023080448000000 2899393205050306844203427097038060148228096000000000 10311371520837939750020808494774745446370520596480000000 10726358985988477485088314676023888680237137920000000000 3632250889870246632618654103669404743238319865856000000 2800065155555720550390780420546106716365783040000000000 10956486622239546113342237669222306011068078489600000000 4519476272847499584750456590252630151087626649600000000 531060540987440027319494484152928478330198425600000000 5991198234517626609584037904869325143874417459200000000 5569032268327716796527092777713523720078111539200000000 529766337986959321245057814325782115641825689600000000 2554674582364897614831343634484168640758074572800000000 9914634522183944053784334105946405212543516672000000000 1232666254438191969052487775268874303978864640000000000 2354523872427055959814560275925242170325487058944000000 93130203433040941980286122287969700425100165120000000 3013590766632777045937774626151210120694344974336000000 1140931545026784614099056504530683883995875246080000000 1568036487111203508218837035505819761164838502400000000 575016733420581971789418628407431686167790092288000000 2460663318518663513979776733207184690139627520000000000 283753871600602521392681621041204715793093230592000000 27157822578968527077368773309644513302544384000000000 6385455774627619755241301852038655576020038451200000000 877256640972292440810706289419593898279305216000000000 2016996287506173461095857772664486854937857228800000000 1948925327161482917975569289521603556434425937920000000 5362098206806135065378321822419603222308061184000000000 6108444549961669188980069202002692069441457356800000000 200956938994723492058843928017254651515843379200000000 10389476167855061247823662080939423300945875467632640000 1078099952941239998011423477429517024483082240000000000 734324682723202743472141958408604992154265190400000000 25139903873410494105675737521930989094305792000000000 132274571149329061294478495884621511850039705600000000 774818788504006380547278030169006705358143488000000000 24273399238144699502795224164176246055560578942894080000 320633061911665592492813895777359141207329996800000000 41228497678173712188199216630024090973468884992000000 8188425833053703794420097364286093590716743680000000000 2524101509190323434821080595448067922830819328000000000 2017090234535223222085889086803612497419960320000000000 2990760229916945278410315023951680508722465996800000000 4165254593039557052105721546088519096481423032320000000 541540213693340815851421688422198414814651351040000000 3953033160784546659375219417241562423104634880000000000 2162134344965847025717116184998399474310683033600000000 979811638143178231810951821367566754444738560000000000 6789837090596373906511586186120434658800167813120000000 49093699100652874479359368458149956169861431296000000 7859958221052966659359741416987584144773207818240000000 908930757192913958187471157996395024471105208320000000 6906753033664394895233044224214377482629939200000000 7395997526629151814314926651613245823873187840000000000 787269049740816349640747822078146061571352166400000000 1824476843439021535096255115649951887586754560000000000 5186003027600679069799394997381192607453937664000000000 35262215379250932506591206382581747883704320000000000 525631253076641162243433535728860749104697835520000000 1001906775090493283474400526386630565834493263872000000 2301992217499638648870373415513687074907230961664000000 16621182415488191133351402122588027187019738251264000000 879575153422648489426199716879836140179292160000000000 3774994259950930392466967832230604101493278638080000000 2545820308421474609415756284894837359465935667200000000 66863838917051467521130308395906377337567969280000000 705898778711526189174146324507421861268684800000000000 3332457397852792742478593001413164014696923136000000000 1270441771728572693679879342651777504054859530240000000 838141903450614799159498181394940219386494976000000000 5319509970530902501230157454407596307302580224000000000 3319964641062732145678218660349750158680496537600000000 20491764667169333676713224508595854469664404846673920000 1618418282297673220544207479058898497929897574400000000 1252886497892292558629732731834681818971834941440000000 3853065166597782591016469621288799204251019509760000000 2377284919273655940315512138018543300530667520000000000 6924396419974264231672259345868136844471618764800000000 1573976590335265717920567914416548882426101760000000000 1230050106406996373031239292752784834250502307840000000 27352217219909048486242178339664803366594150400000000 157419012670622423992815447905016936117829632000000000 1910632694379197552031356051666755171167240192000000000 4758576093342823586509477043339254682987454529536000000 2368737609405788777957002824288608750219034624000000000 1578942111721442449054483991765601090209946009600000000 15843393300951178872550072339421023158185235578880000000 4930665017752767876209951101075497215915458560000000000 140307237885833368550124616336135765021572464640000000 2970812565281788380894560261548502964811648204800000000 1112586113189519118733905292671253351373576601600000000 947919046748973578966299751719331961512971468800000000 1916622138562204440909197293208030265747701760000000000 2770732141030406818440785121155875467820007424000000000 145722243927294442024309036915170476468207616000000000 1646083552080539429442399059897512147467160780800000000 79839914499072887874069100481736877453344768000000000 7927291398375110267401009897514954825090804219904000000 134832607224992670403523678291684120020616478720000000 2930188207195109896535245615745205477513048883200000000 173693881307199777457396004696977742833385472000000000 587307783887989789392889741990174988575545753600000000 10421390484016426260072844702024775252769528348672000000 5378907292093928592229037564809633326453227520000000000 579255308930836083234903183918016250306258534400000000 880337428023118422752811379312535691564920340480000000 1976516580392273329687609708620781211552317440000000000 275184428463623639525665024204574541871180677120000000 5289549788135061884977511572516873896775699660800000000 586609158363194254980100848635315791333844582400000000 152345913110569239352198682078568260017166745600000000 5095020518344526805416949471111347123112640512000000000 845256860186188778778848760184370951299792896000000000 9182626909851747535806433485788870224745689251840000000 521081643921599332372188014090933228500156416000000000 4984259202728341440081798395652404794349322240000000000 33890080237211786213275749801024838529691156480000000 2465332508876383938104975550537748607957729280000000000 2456527749916111138326029209285828077215023104000000000 3840450692039017758937459083588046225323275059200000000 4865271582504057426923346975066538366898012160000000000 9439303282694969416181268499566757936182444687360000000 2986289589227045927072318378286443215966332518400000000 5671164624254727337303811141528727245774454270197760000 2371819896470727995625131650344937453862780928000000000 6863981745974130809777904796706384841299199000576000000 1563689161640263981202132830008597582540963840000000000 1736938813071997774573960046969777428333854720000000000 1368639205666431248459359487679036705087820922880000000 479255692570032830777095999581961999456665600000000000 267183643808859359310121044842953965687118233600000000 2292759233255037062437627262000106205400688230400000000 1505917394584589203571512158949166637373194240000000000 2155839476678376546920907769035191677494912614400000000 2786349192561573935702046021832878330840141004800000000 18577130432464018355012156713397600244046233600000000 2218799257988745544294477995483973747161956352000000000 2487003383748224076166254931984070778160152576000000000 13603380837878998041732818995365089036717352026112000000 218358022214765434517869263047629162419113164800000000 4315782086127128588117886610823729327813060198400000000 2156199905882479996022846954859034048966164480000000000 354035650212152286477721040820683834412289228800000000 2628603365248399116614567487230970623686606848000000000 443645362471949895982513015092899807546572800000000000 1587294853791948735533741950615458142200476467200000000 3169713225698207920420682850691391067374223360000000000 2108284352418424885000117022528833292322471936000000000 203587607792789792874977514445900826647776460800000000 4197270907560708581121514438444130353136271360000000000 11103144570815778188139617891972677529453696385024000000 277067242318422712358469811695246839616897024000000000 1038681662503945877463896839230455187687100907520000000 1258769775120412504867716928156921053945475891200000000 1388788306265064391084907709632857554625514962944000000 2804894989304799413790393000661157497521831936000000000 7297017006858523082371605712943708920221165158400000000 4990046008730471576340842768562309866478690631680000000 3944532014202214300967960880860397772732366848000000000 655074066644296303553607789142887487257339494400000000 1959623276286356463621903642735133508889477120000000000 4138277763107970868568898965839688438373364531200000000 3260892987835935757383241059961493296591971287040000000 535723097980325134376138875178965957487886336000000000 809844313159157518129460178885437827653304320000000000 134338608164614889343913928683466316079693824000000000 432504573353301418741112505108678432648069120000000000 1852734733943464292878890716767762590222778368000000000 398740736218267315206543871652192383547945779200000000 235362507233495496764748787877207235562045440000000000 1819650185123045287648910525396909686825943040000000000 1159217860028485471291751596564612327170637824000000000 2413430771847407434144870802105374953053356032000000000 4370769538796840060149721886853167159161514885120000000 5222891082627653153414608350715043974852632379392000000 127044204101377881777728556990246425613828096000000000 5514337059796138974934468562800847959714393227264000000 1759150306845296978852399433759672280358584320000000000 1310148133288592607107215578285774974514678988800000000 2530967984762053900093484639870247109857902592000000000 3449919849411967993636555127774454478345863168000000000 5401400551034392207915425846557341849524319027200000000 1103742161202818603593624097105271476653444300800000000 369112941576662313457450828557292639878748569600000000 1694157068907662854017951178817812467044843520000000000 3773280285357261749800355304125052232343696179200000000 1111640840366078575727334430060657554133667020800000000 1661419734242780480027266131884134931449774080000000000 379384003907831092867470220785504017241341952000000000 8994772636766131303425245351512326968582382551040000000 233619081253988122714639537596635330113437696000000000 1960573312946774112941281742950400620137912729600000000 2139103959669363240077439850345027817092782489600000000 227956177037392486584588791093678795932041216000000000 3294194300653788882812682847701302019253862400000000000 3135397242058170341795045828376213614223163392000000000 358783967496546146648422064000770767436382208000000000 25892255598588786701723628029363141788827648000000000 2317628041408886401885442530225242774667316428800000000 1022412144149403372324471465774852265507553280000000000 1528506155503358041625084841333404136933792153600000000 1176106071844815384712625213509611281645454753792000000 3011834789169178407143024317898333274746388480000000000 1495277760818502432024539518695721438304796672000000000 4613658465474677157552142123037287378319226961920000000 2958399010651660725725970660645298329549275136000000000 1803097774515280509603396538721479910095847424000000000 1175773965771813878173142185641080105333686272000000000 203731169052053874310930652125778405127880704000000000 1819650185123045287648910525396909686825943040000000000 481672107826688458495299844958005505336279040000000000 476417503014033675311714755740281808914428723200000000 2709508101740153562892539233675895334917636096000000000 946443439940159778096027765531519589432688640000000000 2116393138389264980711655934153944189600635289600000000 2814640490952475166163839094015475648573734912000000000 464121302278347583489398231174110567894876160000000000 4361504057866388597488785792941324516601655984128000000 192668843130675383398119937983202202134511616000000000 3847632586818998867020675206500145013423928770560000000 2126285468752389108817115436543533879549912678400000000 1359343418925911301840490471541564943913451520000000000 677662827563065141607180471527124986817937408000000000 2694633247357364903596283217604468444016211394560000000 1304214491380582676821403913529045921188072652800000000 2646763905633520418398415309668232271746826240000000000 145027861046349889373261852042100589034943283200000000 438176633206887159567630628189222399503237120000000000 3821265388758395104062712103333510342334480384000000000 1292909342061111125434752215413593724850012160000000000 1840978192807566975675537724219620314195165184000000000 577700804642918474145496870310956448926924800000000000 4279152693388235731783545483903336018956255232000000000 1250595945411838397693251233818239748400375398400000000 137153045061932700810007814827144900942548172800000000 433179882126457744590105015762503196701884416000000000 2697174594808423559537233166618102095958507520000000000 405618617117211333469726185227794109756866560000000000 2418735015302017120813321067604507645257868902400000000 1208305261267476712747102641370279950145290240000000000 2855627049290612971736978854051974848001028915200000000 400832033785845640286298472377640945000120320000000000 6447766682098316814386275499034300441140427227136000000 3498274269103912050716246139735235334133252096000000000 1633026483332642840082977540500347647941033328640000000 1150213662168078793865030398996708798695997440000000000 2002470302406554254988824562206054090511745024000000000 2541538943347377218897038869752870038049862451200000000 18862683942863324248766986935418397411770368000000000 2258876091876883805357268238423749956059791360000000000 1123901584928939736489032971568679512451317760000000000 628884364587160975628134603240919819497557196800000000 2223281680732157151454668860121315108267334041600000000 1460363593546916090502283534895893069235748864000000000 3310031834295239662568861937033642612307947159552000000 1178097629735789794928425075336022951391657984000000000 1780136947930068903598201009981640253722591232000000000 1064748869932679750358031236222959538111774720000000000 564922146376387751592377101711028751226109952000000000 3551810118920982539245206766946452806891365990400000000 1381067832811336936266865424403808377693536256000000000 604053173295764801910569727732165865399281254400000000 2044824288298806744648942931549704531015106560000000000 337542765293343697083198713581171322105364480000000000 5259792357626072324437695341478481594068683980800000000 1005596154936419764227029500877239563772231680000000000 1395592576763935603222903550782673342417810227200000000 1833761978084661430946697882035156736674050867200000000 1016526546687794571851870299172390031546258554880000000 1018689785009477010590191903141785364592590848000000000 2544859663358658985858089456281532743611758673920000000 237345676320397211432466590269162133064253440000000000 1892886879880319556192055531063039178865377280000000000 954010378157213815282915649858212339396902912000000000 1593483137822326703313600593697779616439074816000000000 460085464867231517546012159598683519478398976000000000 919555842214587057127390613101646873823805440000000000 1928370258593234817484568670266296219963962163200000000 981748024779824829107020896113352459493048320000000000 903550436750753522142907295369499982423916544000000000 1421557107858135919081406227610321062693385011200000000 1252691649047381122925748364011229844095453102080000000 902208909659989535720042401902110311918338048000000000 2408470321950040967908634905666371231639876403200000000 1832463192407444402393679169686586491080068300800000000 436716044429530869035738526095258324838226329600000000 1417297709978983456814762327143420069983289344000000000 1445435168791219017623721534739197390361303449600000000 425899547973071900143212494489183815244709888000000000 1690513720372377557557697520368741902599585792000000000 1900727212274430275345312703505121206941096345600000000 1667461260549117863591001645090986331200500531200000000 1732962928566316199548773513414011658985222963200000000 352496406182258371898833068355631301632458752000000000 1534252419245851868849239295624131220155347763200000000 1267640143532785026242285900783010336026394624000000000 66303043182621083355628318739158652556410880000000000 814174442450096396115248732225623983366560808960000000 388383833978831800525854420440447126832414720000000000 1741454604925130753448702327484715910803887226880000000 1533618216224105058486707198662278398261329920000000000 1192566798074646883694040647794122814826144071680000000 1317080133993823255822068570763477487607349248000000000 219340289521174635752767460362283364679208140800000000 207556890099863935751611024100086008663087513600000000 182835664533894502586732636523134466140405760000000000 727860074049218115059564210158763874730377216000000000 302076315316869178186775660342569987536322560000000000 949382705281588845729866361076648532257013760000000000 1419665159910239667144041648297279384149032960000000000 115042946195931772037441624826309588107132928000000000 1530781971437368682287874387830732503318968401920000000 172907936142913805613697380241335309607895040000000000 2428517564500691078736859654566098391293283532800000000 849844199221573444553344196886691074640183296000000000 1573462218900515631084646160196151317431844864000000000 303693965468139730903772222269613581981722869760000000 1162993813969946336019086292318894452014841856000000000 455260804689397311440964264942604820689610342400000000 1310148133288592607107215578285774974514678988800000000 1222529683198214039895213416012461592115412992000000000 1864520839360187117826965150486967311633995530240000000 1133782038422820525381244250439612958714626048000000000 59784360149178202433122100196453492103053312000000000 430540760995855375978106476800924920923658649600000000 309414201518898388992932154116073711929917440000000000 613447286489642023394682879464911359304531968000000000 490429782514446430467941660320878332706029568000000000 1206715385923703717072435401052687476526678016000000000 4936282828510397054694325573774380470608456581120000000 56538150548317847549875651317008053617819648000000000 846020691839579966110099233378447817855677235200000000 599337722738636639070580235654889707354141491200000000 962499176867716060045871093696786439610564608000000000 1489344118910492501738727853938992384978190336000000000 567866063964095866857616659318911753659613184000000000 282940259142949863731504804031275961176555520000000000 789006213873190891931976992995987965421289472000000000 21334383464170742594134753990488543026510561280000000 731342658135578010346930546092537864561623040000000000 1544103157090127001233504074408234791392300236800000000 543737367570364520736196188616625977565380608000000000 711954040962478208698996810461238440404975616000000000 221010143942070277852094395797195508521369600000000000 573627692048147164208038906268170192718659584000000000 691631744571655222454789520965341238431580160000000000 517845111971775734034472560587262835776552960000000000 896417143829037046968094869353424982562675097600000000 156199383538083257254904378293524642444764774400000000 4392364628851262268294189788569773335512256348160000000 1196262451247828852794730193346702152881405952000000000 684501475386771933450568111320540719224769740800000000 963344215653376916990599689916011010672558080000000000 223893321728950921931346718142368013564352921600000000 952835006028067350623429511480563617828857446400000000 474691352640794422864933180538324266128506880000000000 195895354857744109914356396274786928007577600000000000 928242604556695166978796462348221135789752320000000000 195372967244790125621251445884720829532890726400000000 513925822607933843546404180346058393224478720000000000 629384887560206252433858464078460526972737945600000000 774178442397804722381536478077957939485946675200000000 185258503010264791728961478830002117437030400000000000 1147293794950188003731747294182668775031046144000000000 876353266413774319135261256378444799006474240000000000 68904935331757274353977975489680181497639731200000000 427222217376714980578439862484491839515656192000000000 85241366960844260533713669531962186398905139200000000 883330186019895885515281565488005334236659712000000000 1084997299296784130225951061014379067789541376000000000 306518614071529019042463537700548957941268480000000000 811237234234422666939452370455588219513733120000000000 804476923949135811381623600701791651017785344000000000 801664067571691280572596944755281890000240640000000000 397818259095726500133769912434951915338465280000000000 1752837612700833949215206331492678511806979768320000000 1735434022143506027802470401710998089345322188800000000 379753082112635538291946544430659412902805504000000000 629878910234900291878469028022007199285903360000000000 377253678857266484975339738708367948235407360000000000 31343256777239057586297023403965908481212416000000000 464121302278347583489398231174110567894876160000000000 613037228143058038084927075401097915882536960000000000 365671329067789005173465273046268932280811520000000000 181245789190121506912065396205541992521793536000000000 29641360481642366676633836612800338789924864000000000 215292836074050144327444627670623672839700480000000000 694775525228799109829584018787910971333541888000000000 345815872285827611227394760482670619215790080000000000 1029219683655561053926331146294673128127515852800000000 389379689963392907706689944595422632285831168000000000 675085530586687394166397427162342644210728960000000000 1183984887280233114120843656899224127752948940800000000 329104196161010104656118745741642039052730368000000000 245214891257223215233970830160439166353014784000000000 321114738551125638996866563305337003557519360000000000 1291474450444759957039909451040880114616657510400000000 318254607276581200107015929947961532270772224000000000 391790709715488219828712792549573856015155200000000000 311234285057244850104655284434403557294211072000000000 621414134366130880841367072704715402931863552000000000 68714062934716395477651166693309876285734912000000000 1153786879502312341834192529401416280516413358080000000 370517006020529583457922957660004234874060800000000000 293943491442953469543285546410270026333421568000000000 292537063254231204138772218437015145824649216000000000 287313187124691361207722714536354161077780480000000000 498425920272834144008179839565240479434932224000000000 276652697828662088981915808386136495372632064000000000 336030854990467261773346886009922325558434201600000000 267221355857230426857532314918427296666746880000000000 132606086365242166711256637478317305112821760000000000 262730240632739159179254460886184821092515840000000000 393365554725128907771161540049037829357961216000000000 806761572460917926753864497134536469667381248000000000 248134116153142539224851435281396775476264960000000000 495062722430237422388691446585717939087867904000000000 459777921107293528563695306550823436911902720000000000 233537991673545919270448409676608729860014080000000000 57462637424938272241544542907270832215556096000000000 561589008182496960570432991987298001248845824000000000 452704414628719781970407686450041537882488832000000000 383954895521178455432138536698582378894852096000000000 327346160925107272900477085775073438416764928000000000 52546048126547831835850892177236964218503168000000000 417910090363187434483960312052878779749498880000000000 363106665900118991788764498506804150176579584000000000 545363339573728280853477047400612770100333772800000000 395218139755231555688451154837337850532331520000000000 385337686261350766796239875966404404269023232000000000 94029770331717172758891070211897725443637248000000000 185648520911339033395759292469644227157950464000000000 420379791019301997588847208158295059717737676800000000 88924081444927100029901509838401016369774592000000000 306518614071529019042463537700548957941268480000000000 344775824549629633449267257443624993293336576000000000 340134611526846157614373275131883887614387814400000000 81738297085741071744656943386813055451004928000000000 320665627028676512229038777902112756000096256000000000 156716283886195287931485117019829542406062080000000000 38174479408175775265361759274061042380963840000000000 297760939383771047069821722337676130571517952000000000 148206802408211833383169183064001693949624320000000000 93415196669418367708179363870643491944005632000000000 166058985425564622404323652842165534357192704000000000 96334421565337691699059968991601101067255808000000000 125975782046980058375693805604401439857180672000000000 250746054217912460690376187231727267849699328000000000 122607445628611607616985415080219583176507392000000000 237130883853138933413070692902402710319398912000000000 114925274849876544483089085814541664431112192000000000 229046876449054651592170555644366254285783040000000000 80166406757169128057259694475528189000024064000000000 105092096253095663671701784354473928437006336000000000 198507292922514031379881148225117420381011968000000000 152697917632703101061447037096244169523855360000000000 83983854697986705583795870402934293238120448000000000 76348958816351550530723518548122084761927680000000000 68714062934716395477651166693309876285734912000000000 122158334106162480849157629676995335619084288000000000 91618750579621860636868222257746501714313216000000000 2751311079906044474925152714400127446480825876480000000000
Conjugacy classes   1 11 15 66 9 297 6 125 35 118 4 1402 3 64 117 83 2 428 2 433 65 28 2 1435 5 21 12 211 1 1556 1 13 29 13 27 1098 1 10 22 437 1 730 1 82 124 5 492 18 13 59 34 13 221 11 4 4068 3 71 11 273 33 7 250 768 2 22 25 9 186 172 1 1827 7 5 89 1026 7 15 5 6 25 32 28 98 62 202 48 102 3 87 73 4 8 23 5 2553 1 6 492 2 73 637 4 17 32 43 534 4 193 3 2 64 23 14 55 3 424 9 3 84 1176 39 12 18 6 33 1641 38 13 1 13 3 10 27 61 175 17 2 204 2 7 22 2 1603 19 2 202 2 2 4 11 146 16 47 5 117 19 574 2 3 748 2 35 1 134 3 399 14 28 10 34 3 73 3 365 28 14 3 7 3 1 72 7 54 97 4 256 121 1 9 1 2 553 2 262 65 1 36 19 20 11 3 1 20 802 66 3 1 11 7 1 13 47 20 359 1 250 15 2 1 3 113 16 6 2492 1 15 1 2 7 1 134 5 1 14 14 75 1 24 259 6 157 1 32 7 9 2 3 51 373 3 163 2 88 4 12 83 23 22 168 3 32 2 1 89 8 112 25 6 38 4 9 2 24 4 65 68 4 50 6 576 1 12 2 2 2 805 6 7 3 39 1 43 50 27 6 11 1 76 7 127 44 4 3 12 1 9 4 27 21 92 501 1 120 52 4 3 19 21 4 16 9 1114 1 15 56 2 10 1 29 8 3 9 60 11 12 360 4 4 72 5 20 2 23 3 4 6 181 5 57 4 2 203 2 7 18 2 4 15 14 10 6 1 224 3 3 3 1 1 24 2 126 16 65 2 110 2 2 27 3 7 1 3 28 15 2 1 17 587 2 2 1 9 6 3 2 2 3 3 2 342 16 18 7 46 16 43 83 2 3 1 90 21 4 9 2 10 3 2 7 2 7 4 41 110 2 202 1 4 16 2 55 7 2 1 49 3 5 5 154 5 23 71 2 5 2 5 1 24 3 2 68 2 1 152 2 9 9 3 3 3 1 17 3 2 2 3 174 3 18 10 2 1 71 6 2 5 1 11 2 18 18 90 1 5 2 28 1 2 3 40 3 250 99 28 1 10 8 1 2 2 4 2 15 214 2 14 1 4 41 15 17 2 1 147 1 10 77 10 31 23 2 2 3 9 1 1 10 4 1 30 52 3 22 7 1 17 6 1 2 44 2 7 4 16 26 1 26 1 51 2 31 17 4 8 2 1 2 4 2 4 58 2 30 11 5 15 4 5 2 13 41 9 3 5 1 1 8 2 221 3 31 11 7 7 1 1 3 4 4 19 1 11 2 4 4 1 6 6 124 26 13 2 9 2 1 2 2 4 18 8 6 2 7 2 5 1 2 14 7 3 2 4 2 1 41 35 1 3 1 1 2 3 1 1 1 5 4 1 16 4 2 22 1 3 3 31 1 2 1 2 3 64 2 1 1 1 3 1 5 3 1 1 5 33 1 2 7 1 1 12 2 3 5 1 2 3 26 2 7 1 1 7 1 3 3 12 1 7 1 1 3 1 2 4 2 1 2 1 2 1 3 2 1 6 4 2 1 1 2 2 52887
Divisions 1 11 15 66 9 297 6 125 35 118 4 1402 3 64 117 83 2 428 2 433 65 28 2 1435 5 21 12 211 1 1556 1 13 29 13 27 1098 1 10 22 437 1 730 1 82 123 5 492 18 13 59 34 13 221 11 4 4068 3 71 11 273 33 7 250 768 2 21 25 9 186 172 1 1827 7 5 89 1026 7 15 5 6 25 31 28 98 62 200 48 102 3 87 73 4 8 23 5 2553 1 6 492 1 73 637 4 16 32 43 534 4 193 3 2 64 23 14 55 3 424 9 3 84 1176 39 12 18 6 33 1641 38 13 1 13 3 9 27 61 175 17 2 204 1 7 22 2 1603 19 2 202 2 2 4 11 146 16 47 5 117 19 574 2 3 748 2 35 1 134 3 399 14 28 10 33 3 73 3 365 28 14 3 7 3 1 72 7 54 97 4 256 119 1 9 1 2 553 1 262 65 1 36 18 20 11 3 1 19 802 66 3 1 11 7 1 13 47 19 359 1 250 15 2 1 3 113 16 6 2492 1 14 1 2 7 1 134 5 1 14 14 75 1 24 259 5 157 1 32 7 9 1 3 51 373 3 163 1 88 4 11 83 23 22 168 3 32 1 1 89 8 112 25 6 37 4 9 2 24 4 65 68 4 50 6 576 1 12 2 2 2 805 6 7 3 39 1 43 50 27 6 11 1 76 7 127 44 4 3 12 1 9 4 27 20 92 501 1 120 52 4 3 19 20 4 16 9 1114 1 14 56 2 10 1 29 8 3 9 60 11 12 360 4 4 72 5 20 2 23 3 3 6 181 5 57 4 2 203 1 7 18 2 4 15 14 10 6 1 224 3 3 3 1 1 24 1 126 16 64 2 110 2 2 27 3 7 1 3 28 15 2 1 17 587 2 1 1 9 6 3 2 2 2 3 1 342 16 18 7 45 16 43 83 1 3 1 90 21 4 9 2 10 2 2 7 2 7 4 41 110 2 202 1 3 16 1 55 7 2 1 49 3 5 5 154 5 23 71 2 5 1 5 1 23 3 2 68 1 1 152 2 9 9 3 3 3 1 17 3 2 1 3 174 3 16 10 2 1 71 6 1 5 1 11 2 18 18 90 1 5 2 28 1 1 2 40 3 250 99 28 1 10 7 1 2 2 4 1 15 214 2 14 1 4 41 15 17 1 1 147 1 10 77 9 31 23 2 1 3 9 1 1 9 4 1 30 52 3 22 6 1 17 6 1 1 44 2 6 4 16 26 1 24 1 51 2 31 17 4 8 2 1 2 4 2 4 58 2 30 11 5 15 4 5 2 13 41 9 3 5 1 1 8 2 221 3 31 11 7 7 1 1 3 4 4 19 1 11 2 4 4 1 6 6 124 26 13 2 9 1 1 2 2 4 18 8 6 2 7 1 5 1 2 14 7 3 1 4 2 1 41 35 1 3 1 1 2 3 1 1 1 5 4 1 16 4 1 22 1 2 3 31 1 2 1 1 3 64 2 1 1 1 3 1 5 3 1 1 5 33 1 1 7 1 1 12 1 3 5 1 1 3 26 1 7 1 1 6 1 3 3 12 1 7 1 1 3 1 2 4 2 1 1 1 1 1 3 2 1 6 4 2 1 1 1 2 52815
Autjugacy classes 1 11 15 66 9 297 6 125 35 118 4 1402 3 64 117 83 2 428 2 433 65 28 2 1435 5 21 12 211 1 1556 1 13 29 13 27 1098 1 10 22 437 1 730 1 82 123 5 492 18 13 59 34 13 221 11 4 4068 3 71 11 273 33 7 250 768 2 21 25 9 186 172 1 1827 7 5 89 1026 7 15 5 6 25 31 28 98 62 200 48 102 3 87 73 4 8 23 5 2553 1 6 492 1 73 637 4 16 32 43 534 4 193 3 2 64 23 14 55 3 424 9 3 84 1176 39 12 18 6 33 1641 38 13 1 13 3 9 27 61 175 17 2 204 1 7 22 2 1603 19 2 202 2 2 4 11 146 16 47 5 117 19 574 2 3 748 2 35 1 134 3 399 14 28 10 33 3 73 3 365 28 14 3 7 3 1 72 7 54 97 4 256 119 1 9 1 2 553 1 262 65 1 36 18 20 11 3 1 19 802 66 3 1 11 7 1 13 47 19 359 1 250 15 2 1 3 113 16 6 2492 1 14 1 2 7 1 134 5 1 14 14 75 1 24 259 5 157 1 32 7 9 1 3 51 373 3 163 1 88 4 11 83 23 22 168 3 32 1 1 89 8 112 25 6 37 4 9 2 24 4 65 68 4 50 6 576 1 12 2 2 2 805 6 7 3 39 1 43 50 27 6 11 1 76 7 127 44 4 3 12 1 9 4 27 20 92 501 1 120 52 4 3 19 20 4 16 9 1114 1 14 56 2 10 1 29 8 3 9 60 11 12 360 4 4 72 5 20 2 23 3 3 6 181 5 57 4 2 203 1 7 18 2 4 15 14 10 6 1 224 3 3 3 1 1 24 1 126 16 64 2 110 2 2 27 3 7 1 3 28 15 2 1 17 587 2 1 1 9 6 3 2 2 2 3 1 342 16 18 7 45 16 43 83 1 3 1 90 21 4 9 2 10 2 2 7 2 7 4 41 110 2 202 1 3 16 1 55 7 2 1 49 3 5 5 154 5 23 71 2 5 1 5 1 23 3 2 68 1 1 152 2 9 9 3 3 3 1 17 3 2 1 3 174 3 16 10 2 1 71 6 1 5 1 11 2 18 18 90 1 5 2 28 1 1 2 40 3 250 99 28 1 10 7 1 2 2 4 1 15 214 2 14 1 4 41 15 17 1 1 147 1 10 77 9 31 23 2 1 3 9 1 1 9 4 1 30 52 3 22 6 1 17 6 1 1 44 2 6 4 16 26 1 24 1 51 2 31 17 4 8 2 1 2 4 2 4 58 2 30 11 5 15 4 5 2 13 41 9 3 5 1 1 8 2 221 3 31 11 7 7 1 1 3 4 4 19 1 11 2 4 4 1 6 6 124 26 13 2 9 1 1 2 2 4 18 8 6 2 7 1 5 1 2 14 7 3 1 4 2 1 41 35 1 3 1 1 2 3 1 1 1 5 4 1 16 4 1 22 1 2 3 31 1 2 1 1 3 64 2 1 1 1 3 1 5 3 1 1 5 33 1 1 7 1 1 12 1 3 5 1 1 3 26 1 7 1 1 6 1 3 3 12 1 7 1 1 3 1 2 4 2 1 1 1 1 1 3 2 1 6 4 2 1 1 1 2 52815

Minimal presentations

Permutation degree:$46$
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 $46$ $\langle(1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46), (1,2,3)\rangle$ Copy content Toggle raw display
Copy content comment:Define the group as a permutation group
 
Copy content magma:G := PermutationGroup< 46 | (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), (1,2,3) >;
 
Copy content gap:G := Group( (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), (1,2,3) );
 
Copy content sage:G = PermutationGroup(['(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)', '(1,2,3)'])
 
Transitive group: 46T55 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 46.

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 $52887 \times 52887$ character table is not available for this group.

Rational character table

The $52815 \times 52815$ rational character table is not available for this group.