Finite Group Databasebeta

?

← Prev (#49119478) Next (#49119480) →

Dic₉₀₅₆ #49119479

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 411 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64)(65,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66)(129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411);(1,65,33,97)(2,66,34,98)(3,67,35,99)(4,68,36,100)(5,69,37,101)(6,70,38,102)(7,71,39,103)(8,72,40,104)(9,73,41,105)(10,74,42,106)(11,75,43,107)(12,76,44,108)(13,77,45,109)(14,78,46,110)(15,79,47,111)(16,80,48,112)(17,81,49,113)(18,82,50,114)(19,83,51,115)(20,84,52,116)(21,85,53,117)(22,86,54,118)(23,87,55,119)(24,88,56,120)(25,89,57,121)(26,90,58,122)(27,91,59,123)(28,92,60,124)(29,93,61,125)(30,94,62,126)(31,95,63,127)(32,96,64,128)(130,411)(131,410)(132,409)(133,408)(134,407)(135,406)(136,405)(137,404)(138,403)(139,402)(140,401)(141,400)(142,399)(143,398)(144,397)(145,396)(146,395)(147,394)(148,393)(149,392)(150,391)(151,390)(152,389)(153,388)(154,387)(155,386)(156,385)(157,384)(158,383)(159,382)(160,381)(161,380)(162,379)(163,378)(164,377)(165,376)(166,375)(167,374)(168,373)(169,372)(170,371)(171,370)(172,369)(173,368)(174,367)(175,366)(176,365)(177,364)(178,363)(179,362)(180,361)(181,360)(182,359)(183,358)(184,357)(185,356)(186,355)(187,354)(188,353)(189,352)(190,351)(191,350)(192,349)(193,348)(194,347)(195,346)(196,345)(197,344)(198,343)(199,342)(200,341)(201,340)(202,339)(203,338)(204,337)(205,336)(206,335)(207,334)(208,333)(209,332)(210,331)(211,330)(212,329)(213,328)(214,327)(215,326)(216,325)(217,324)(218,323)(219,322)(220,321)(221,320)(222,319)(223,318)(224,317)(225,316)(226,315)(227,314)(228,313)(229,312)(230,311)(231,310)(232,309)(233,308)(234,307)(235,306)(236,305)(237,304)(238,303)(239,302)(240,301)(241,300)(242,299)(243,298)(244,297)(245,296)(246,295)(247,294)(248,293)(249,292)(250,291)(251,290)(252,289)(253,288)(254,287)(255,286)(256,285)(257,284)(258,283)(259,282)(260,281)(261,280)(262,279)(263,278)(264,277)(265,276)(266,275)(267,274)(268,273)(269,272)(270,271)

Polycyclic presentation:

2^7,283|a^2=g,b^2=g,c^2=de,d^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=cd,d^a=de,e^a=ef,f^a=fg,h^a=h^282,c^b=cd,d^b=de,e^b=ef,f^b=fg,h^b=h^282

Conjugacy classes & character table

9059 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36224, 2728);