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Dic₅₇₄₄ #37526284

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

Aliases

Splittings

Subgroups

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 423 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)(33,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423);(1,33,17,49)(2,34,18,50)(3,35,19,51)(4,36,20,52)(5,37,21,53)(6,38,22,54)(7,39,23,55)(8,40,24,56)(9,41,25,57)(10,42,26,58)(11,43,27,59)(12,44,28,60)(13,45,29,61)(14,46,30,62)(15,47,31,63)(16,48,32,64)(66,423)(67,422)(68,421)(69,420)(70,419)(71,418)(72,417)(73,416)(74,415)(75,414)(76,413)(77,412)(78,411)(79,410)(80,409)(81,408)(82,407)(83,406)(84,405)(85,404)(86,403)(87,402)(88,401)(89,400)(90,399)(91,398)(92,397)(93,396)(94,395)(95,394)(96,393)(97,392)(98,391)(99,390)(100,389)(101,388)(102,387)(103,386)(104,385)(105,384)(106,383)(107,382)(108,381)(109,380)(110,379)(111,378)(112,377)(113,376)(114,375)(115,374)(116,373)(117,372)(118,371)(119,370)(120,369)(121,368)(122,367)(123,366)(124,365)(125,364)(126,363)(127,362)(128,361)(129,360)(130,359)(131,358)(132,357)(133,356)(134,355)(135,354)(136,353)(137,352)(138,351)(139,350)(140,349)(141,348)(142,347)(143,346)(144,345)(145,344)(146,343)(147,342)(148,341)(149,340)(150,339)(151,338)(152,337)(153,336)(154,335)(155,334)(156,333)(157,332)(158,331)(159,330)(160,329)(161,328)(162,327)(163,326)(164,325)(165,324)(166,323)(167,322)(168,321)(169,320)(170,319)(171,318)(172,317)(173,316)(174,315)(175,314)(176,313)(177,312)(178,311)(179,310)(180,309)(181,308)(182,307)(183,306)(184,305)(185,304)(186,303)(187,302)(188,301)(189,300)(190,299)(191,298)(192,297)(193,296)(194,295)(195,294)(196,293)(197,292)(198,291)(199,290)(200,289)(201,288)(202,287)(203,286)(204,285)(205,284)(206,283)(207,282)(208,281)(209,280)(210,279)(211,278)(212,277)(213,276)(214,275)(215,274)(216,273)(217,272)(218,271)(219,270)(220,269)(221,268)(222,267)(223,266)(224,265)(225,264)(226,263)(227,262)(228,261)(229,260)(230,259)(231,258)(232,257)(233,256)(234,255)(235,254)(236,253)(237,252)(238,251)(239,250)(240,249)(241,248)(242,247)(243,246)(244,245)

Polycyclic presentation:

2^6,359|a^2=f,b^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,g^a=g^358,c^b=cd,d^b=de,e^b=ef,g^b=g^358

Conjugacy classes & character table

5747 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22976, 390);