Finite Group Databasebeta

?

← Prev (#46828476) Next (#46828478) →

D₁₇₂₄₉ #46828477

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

Aliases

Splittings

Subgroups

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 414 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)(48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414);(2,47)(3,46)(4,45)(5,44)(6,43)(7,42)(8,41)(9,40)(10,39)(11,38)(12,37)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(49,414)(50,413)(51,412)(52,411)(53,410)(54,409)(55,408)(56,407)(57,406)(58,405)(59,404)(60,403)(61,402)(62,401)(63,400)(64,399)(65,398)(66,397)(67,396)(68,395)(69,394)(70,393)(71,392)(72,391)(73,390)(74,389)(75,388)(76,387)(77,386)(78,385)(79,384)(80,383)(81,382)(82,381)(83,380)(84,379)(85,378)(86,377)(87,376)(88,375)(89,374)(90,373)(91,372)(92,371)(93,370)(94,369)(95,368)(96,367)(97,366)(98,365)(99,364)(100,363)(101,362)(102,361)(103,360)(104,359)(105,358)(106,357)(107,356)(108,355)(109,354)(110,353)(111,352)(112,351)(113,350)(114,349)(115,348)(116,347)(117,346)(118,345)(119,344)(120,343)(121,342)(122,341)(123,340)(124,339)(125,338)(126,337)(127,336)(128,335)(129,334)(130,333)(131,332)(132,331)(133,330)(134,329)(135,328)(136,327)(137,326)(138,325)(139,324)(140,323)(141,322)(142,321)(143,320)(144,319)(145,318)(146,317)(147,316)(148,315)(149,314)(150,313)(151,312)(152,311)(153,310)(154,309)(155,308)(156,307)(157,306)(158,305)(159,304)(160,303)(161,302)(162,301)(163,300)(164,299)(165,298)(166,297)(167,296)(168,295)(169,294)(170,293)(171,292)(172,291)(173,290)(174,289)(175,288)(176,287)(177,286)(178,285)(179,284)(180,283)(181,282)(182,281)(183,280)(184,279)(185,278)(186,277)(187,276)(188,275)(189,274)(190,273)(191,272)(192,271)(193,270)(194,269)(195,268)(196,267)(197,266)(198,265)(199,264)(200,263)(201,262)(202,261)(203,260)(204,259)(205,258)(206,257)(207,256)(208,255)(209,254)(210,253)(211,252)(212,251)(213,250)(214,249)(215,248)(216,247)(217,246)(218,245)(219,244)(220,243)(221,242)(222,241)(223,240)(224,239)(225,238)(226,237)(227,236)(228,235)(229,234)(230,233)(231,232)

Polycyclic presentation:

2,47,367|b^a=b^46,c^a=c^366

Conjugacy classes & character table

8626 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34498, 3);