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D₁₆₉₆₇ #46800296

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

Aliases

Splittings

Subgroups

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 408 points:

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

Polycyclic presentation:

2,19,47,19|b^19=d^18,b^a=b^18d,c^a=c^46,d^a=d^18

Conjugacy classes & character table

8485 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33934, 4);