Finite Group Databasebeta

?

← Prev (#49093520) Next (#49093522) →

Dic₈₉₉₂ #49093521

• 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 409 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);(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)(130,409)(131,408)(132,407)(133,406)(134,405)(135,404)(136,403)(137,402)(138,401)(139,400)(140,399)(141,398)(142,397)(143,396)(144,395)(145,394)(146,393)(147,392)(148,391)(149,390)(150,389)(151,388)(152,387)(153,386)(154,385)(155,384)(156,383)(157,382)(158,381)(159,380)(160,379)(161,378)(162,377)(163,376)(164,375)(165,374)(166,373)(167,372)(168,371)(169,370)(170,369)(171,368)(172,367)(173,366)(174,365)(175,364)(176,363)(177,362)(178,361)(179,360)(180,359)(181,358)(182,357)(183,356)(184,355)(185,354)(186,353)(187,352)(188,351)(189,350)(190,349)(191,348)(192,347)(193,346)(194,345)(195,344)(196,343)(197,342)(198,341)(199,340)(200,339)(201,338)(202,337)(203,336)(204,335)(205,334)(206,333)(207,332)(208,331)(209,330)(210,329)(211,328)(212,327)(213,326)(214,325)(215,324)(216,323)(217,322)(218,321)(219,320)(220,319)(221,318)(222,317)(223,316)(224,315)(225,314)(226,313)(227,312)(228,311)(229,310)(230,309)(231,308)(232,307)(233,306)(234,305)(235,304)(236,303)(237,302)(238,301)(239,300)(240,299)(241,298)(242,297)(243,296)(244,295)(245,294)(246,293)(247,292)(248,291)(249,290)(250,289)(251,288)(252,287)(253,286)(254,285)(255,284)(256,283)(257,282)(258,281)(259,280)(260,279)(261,278)(262,277)(263,276)(264,275)(265,274)(266,273)(267,272)(268,271)(269,270)

Polycyclic presentation:

2^7,281|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^280,c^b=cd,d^b=de,e^b=ef,f^b=fg,h^b=h^280

Conjugacy classes & character table

8995 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35968, 2728);