Finite Group DatabasebetaFinite Group Databasebeta| order | 12832 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C401 ⋊ #131 |
62 conjugacy classes of subgroups.
| minimal degree | μ(G) = 417 |
| transitive degree | μt(G) = 6416 |
A minimal faithful permutation representation — 3 generators on 417 points:
(1,2)(3,11)(4,5)(6,7)(8,24)(9,10)(12,20)(13,14)(15,16)(17,41)(18,19)(21,37)(22,23)(25,33)(26,27)(28,29)(30,62)(31,32)(34,58)(35,36)(38,54)(39,40)(42,50)(43,44)(45,46)(47,87)(48,49)(51,83)(52,53)(55,79)(56,57)(59,75)(60,61)(63,71)(64,65)(66,67)(68,116)(69,70)(72,112)(73,74)(76,108)(77,78)(80,104)(81,82)(84,100)(85,86)(88,96)(89,90)(91,92)(93,149)(94,95)(97,145)(98,99)(101,141)(102,103)(105,137)(106,107)(109,133)(110,111)(113,129)(114,115)(117,125)(118,119)(120,121)(122,186)(123,124)(126,182)(127,128)(130,178)(131,132)(134,174)(135,136)(138,170)(139,140)(142,166)(143,144)(146,162)(147,148)(150,158)(151,152)(153,154)(155,227)(156,157)(159,223)(160,161)(163,219)(164,165)(167,215)(168,169)(171,211)(172,173)(175,207)(176,177)(179,203)(180,181)(183,199)(184,185)(187,195)(188,189)(190,191)(192,265)(193,194)(196,262)(197,198)(200,258)(201,202)(204,254)(205,206)(208,250)(209,210)(212,246)(213,214)(216,242)(217,218)(220,238)(221,222)(224,234)(225,226)(228,229)(231,296)(232,233)(235,293)(236,237)(239,289)(240,241)(243,285)(244,245)(247,281)(248,249)(251,277)(252,253)(255,273)(256,257)(259,269)(260,261)(263,264)(266,323)(267,268)(270,320)(271,272)(274,316)(275,276)(278,312)(279,280)(282,308)(283,284)(286,304)(287,288)(290,300)(291,292)(294,295)(297,346)(298,299)(301,343)(302,303)(305,339)(306,307)(309,335)(310,311)(313,331)(314,315)(317,327)(318,319)(321,322)(324,365)(325,326)(328,362)(329,330)(332,358)(333,334)(336,354)(337,338)(340,350)(341,342)(344,345)(347,380)(348,349)(351,377)(352,353)(355,373)(356,357)(359,369)(360,361)(363,364)(366,391)(367,368)(370,388)(371,372)(374,384)(375,376)(378,379)(381,398)(382,383)(385,395)(386,387)(389,390)(392,401)(393,394)(396,397)(399,400)(404,410)(407,413)(411,416)(414,417);(2,4)(3,6)(5,9)(7,13)(8,15)(10,18)(11,12)(14,22)(16,26)(17,28)(19,31)(20,25)(21,24)(23,35)(27,39)(29,43)(30,45)(32,48)(33,42)(34,41)(36,52)(37,38)(40,56)(44,60)(46,64)(47,66)(49,69)(50,63)(51,62)(53,73)(54,59)(55,58)(57,77)(61,81)(65,85)(67,89)(68,91)(70,94)(71,88)(72,87)(74,98)(75,84)(76,83)(78,102)(79,80)(82,106)(86,110)(90,114)(92,118)(93,120)(95,123)(96,117)(97,116)(99,127)(100,113)(101,112)(103,131)(104,109)(105,108)(107,135)(111,139)(115,143)(119,147)(121,151)(122,153)(124,156)(125,150)(126,149)(128,160)(129,146)(130,145)(132,164)(133,142)(134,141)(136,168)(137,138)(140,172)(144,176)(148,180)(152,184)(154,188)(155,190)(157,193)(158,187)(159,186)(161,197)(162,183)(163,182)(165,201)(166,179)(167,178)(169,205)(170,175)(171,174)(173,209)(177,213)(181,217)(185,221)(189,225)(191,228)(192,230)(194,195)(196,227)(198,232)(199,224)(200,223)(202,236)(203,220)(204,219)(206,240)(207,216)(208,215)(210,244)(211,212)(214,248)(218,252)(222,256)(226,260)(229,263)(231,265)(233,234)(235,262)(237,267)(238,259)(239,258)(241,271)(242,255)(243,254)(245,275)(246,251)(247,250)(249,279)(253,283)(257,287)(261,291)(264,294)(266,296)(268,269)(270,293)(272,298)(273,290)(274,289)(276,302)(277,286)(278,285)(280,306)(281,282)(284,310)(288,314)(292,318)(295,321)(297,323)(299,300)(301,320)(303,325)(304,317)(305,316)(307,329)(308,313)(309,312)(311,333)(315,337)(319,341)(322,344)(324,346)(326,327)(328,343)(330,348)(331,340)(332,339)(334,352)(335,336)(338,356)(342,360)(345,363)(347,365)(349,350)(351,362)(353,367)(354,359)(355,358)(357,371)(361,375)(364,378)(366,380)(368,369)(370,377)(372,382)(373,374)(376,386)(379,389)(381,391)(383,384)(385,388)(387,393)(390,396)(392,398)(394,395)(397,400)(399,401)(402,404)(403,407)(405,411)(406,410)(408,414)(409,413)(412,416)(415,417);(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,91)(53,72,73,87)(57,76,77,83)(61,80,81,79)(65,84,85,75)(67,88,89,71)(70,93,94,120)(74,97,98,116)(78,101,102,112)(82,105,106,108)(86,109,110,104)(90,113,114,100)(92,117,118,96)(95,122,123,153)(99,126,127,149)(103,130,131,145)(107,134,135,141)(111,138,139,137)(115,142,143,133)(119,146,147,129)(121,150,151,125)(124,155,156,190)(128,159,160,186)(132,163,164,182)(136,167,168,178)(140,171,172,174)(144,175,176,170)(148,179,180,166)(152,183,184,162)(154,187,188,158)(157,192,193,230)(161,196,197,227)(165,200,201,223)(169,204,205,219)(173,208,209,215)(177,212,213,211)(181,216,217,207)(185,220,221,203)(189,224,225,199)(191,194,228,195)(198,231,232,265)(202,235,236,262)(206,239,240,258)(210,243,244,254)(214,247,248,250)(218,251,252,246)(222,255,256,242)(226,259,260,238)(229,233,263,234)(237,266,267,296)(241,270,271,293)(245,274,275,289)(249,278,279,285)(253,282,283,281)(257,286,287,277)(261,290,291,273)(264,268,294,269)(272,297,298,323)(276,301,302,320)(280,305,306,316)(284,309,310,312)(288,313,314,308)(292,317,318,304)(295,299,321,300)(303,324,325,346)(307,328,329,343)(311,332,333,339)(315,336,337,335)(319,340,341,331)(322,326,344,327)(330,347,348,365)(334,351,352,362)(338,355,356,358)(342,359,360,354)(345,349,363,350)(353,366,367,380)(357,370,371,377)(361,374,375,373)(364,368,378,369)(372,381,382,391)(376,385,386,388)(379,383,389,384)(387,392,393,398)(390,394,396,395)(397,399,400,401)(402,403,405,408,406,409,412,415)(404,407,411,414,410,413,416,417)Polycyclic presentation:
2^5,401|a^2=d,d^2=e,f^a=f^20,c^b=ce,f^b=f^400,f^c=f^400,f^d=f^400520 conjugacy classes — view the full character table.
| maximal subgroup of | #38787157, #38787158, #38787159, … |
| maximal normal subgroup of | #38787157, #38787158, #38787159, … |
| maximal quotient of | #38787079, #38787089, #38787121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12832, 234);