Finite Group DatabasebetaFinite Group Databasebeta| order | 12448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C389 ⋊ #131 |
62 conjugacy classes of subgroups.
| minimal degree | μ(G) = 405 |
| transitive degree | μt(G) = 6224 |
A minimal faithful permutation representation — 3 generators on 405 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)(192,272)(193,194)(196,268)(197,198)(200,264)(201,202)(204,260)(205,206)(208,256)(209,210)(212,252)(213,214)(216,248)(217,218)(220,244)(221,222)(224,240)(225,226)(228,236)(229,230)(231,232)(233,321)(234,235)(237,317)(238,239)(241,313)(242,243)(245,309)(246,247)(249,305)(250,251)(253,301)(254,255)(257,297)(258,259)(261,293)(262,263)(265,289)(266,267)(269,285)(270,271)(273,281)(274,275)(276,277)(278,363)(279,280)(282,359)(283,284)(286,357)(287,288)(290,355)(291,292)(294,353)(295,296)(298,351)(299,300)(302,349)(303,304)(306,346)(307,308)(310,342)(311,312)(314,338)(315,316)(318,334)(319,320)(322,330)(323,324)(325,326)(327,356)(328,329)(331,354)(332,333)(335,352)(336,337)(339,350)(340,341)(343,347)(344,345)(358,371)(360,370)(361,362)(364,369)(365,366)(367,368)(372,381)(373,374)(375,380)(376,377)(378,379)(382,387)(383,384)(385,386)(388,389)(392,398)(395,401)(399,404)(402,405);(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)(191,229)(192,231)(194,234)(195,228)(196,227)(198,238)(199,224)(200,223)(202,242)(203,220)(204,219)(206,246)(207,216)(208,215)(210,250)(211,212)(214,254)(218,258)(222,262)(226,266)(230,270)(232,274)(233,276)(235,279)(236,273)(237,272)(239,283)(240,269)(241,268)(243,287)(244,265)(245,264)(247,291)(248,261)(249,260)(251,295)(252,257)(253,256)(255,299)(259,303)(263,307)(267,311)(271,315)(275,319)(277,323)(278,325)(280,328)(281,322)(282,321)(284,332)(285,318)(286,317)(288,336)(289,314)(290,313)(292,340)(293,310)(294,309)(296,344)(297,306)(298,305)(300,348)(301,302)(304,345)(308,341)(312,337)(316,333)(320,329)(324,361)(326,365)(327,367)(330,364)(331,363)(334,360)(335,359)(338,358)(339,357)(342,356)(343,355)(346,354)(347,353)(349,352)(350,351)(362,373)(366,376)(368,378)(369,374)(370,375)(371,372)(377,383)(379,385)(380,384)(381,382)(386,389)(387,388)(390,392)(391,395)(393,399)(394,398)(396,402)(397,401)(400,404)(403,405);(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)(157,192,193,231)(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)(191,228,229,195)(194,233,234,276)(198,237,238,272)(202,241,242,268)(206,245,246,264)(210,249,250,260)(214,253,254,256)(218,257,258,252)(222,261,262,248)(226,265,266,244)(230,269,270,240)(232,273,274,236)(235,278,279,325)(239,282,283,321)(243,286,287,317)(247,290,291,313)(251,294,295,309)(255,298,299,305)(259,302,303,301)(263,306,307,297)(267,310,311,293)(271,314,315,289)(275,318,319,285)(277,322,323,281)(280,327,328,367)(284,331,332,363)(288,335,336,359)(292,339,340,357)(296,343,344,355)(300,347,348,353)(304,350,345,351)(308,352,341,349)(312,354,337,346)(316,356,333,342)(320,358,329,338)(324,360,361,334)(326,364,365,330)(362,372,373,371)(366,375,376,370)(368,374,378,369)(377,382,383,381)(379,384,385,380)(386,388,389,387)(390,391,393,396,394,397,400,403)(392,395,399,402,398,401,404,405)Polycyclic presentation:
2^5,389|a^2=d,d^2=e,f^a=f^115,c^b=ce,f^b=f^388,f^c=f^388,f^d=f^388505 conjugacy classes — view the full character table.
| maximal subgroup of | #38735142, #38735143, #38735144, … |
| maximal normal subgroup of | #38735142, #38735143, #38735144, … |
| maximal quotient of | #38735064, #38735074, #38735106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12448, 234);