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Dic₈₄₁₆ #46780965

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

Polycyclic presentation:

2^7,263|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^262,c^b=cd,d^b=de,e^b=ef,f^b=fg,h^b=h^262

Conjugacy classes & character table

8419 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33664, 2728);