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Dic439 #13182182
Aliases
Splittings
Subgroups
6 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 443 points:
(1,2)(3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443);(1,3,2,4)(6,443)(7,442)(8,441)(9,440)(10,439)(11,438)(12,437)(13,436)(14,435)(15,434)(16,433)(17,432)(18,431)(19,430)(20,429)(21,428)(22,427)(23,426)(24,425)(25,424)(26,423)(27,422)(28,421)(29,420)(30,419)(31,418)(32,417)(33,416)(34,415)(35,414)(36,413)(37,412)(38,411)(39,410)(40,409)(41,408)(42,407)(43,406)(44,405)(45,404)(46,403)(47,402)(48,401)(49,400)(50,399)(51,398)(52,397)(53,396)(54,395)(55,394)(56,393)(57,392)(58,391)(59,390)(60,389)(61,388)(62,387)(63,386)(64,385)(65,384)(66,383)(67,382)(68,381)(69,380)(70,379)(71,378)(72,377)(73,376)(74,375)(75,374)(76,373)(77,372)(78,371)(79,370)(80,369)(81,368)(82,367)(83,366)(84,365)(85,364)(86,363)(87,362)(88,361)(89,360)(90,359)(91,358)(92,357)(93,356)(94,355)(95,354)(96,353)(97,352)(98,351)(99,350)(100,349)(101,348)(102,347)(103,346)(104,345)(105,344)(106,343)(107,342)(108,341)(109,340)(110,339)(111,338)(112,337)(113,336)(114,335)(115,334)(116,333)(117,332)(118,331)(119,330)(120,329)(121,328)(122,327)(123,326)(124,325)(125,324)(126,323)(127,322)(128,321)(129,320)(130,319)(131,318)(132,317)(133,316)(134,315)(135,314)(136,313)(137,312)(138,311)(139,310)(140,309)(141,308)(142,307)(143,306)(144,305)(145,304)(146,303)(147,302)(148,301)(149,300)(150,299)(151,298)(152,297)(153,296)(154,295)(155,294)(156,293)(157,292)(158,291)(159,290)(160,289)(161,288)(162,287)(163,286)(164,285)(165,284)(166,283)(167,282)(168,281)(169,280)(170,279)(171,278)(172,277)(173,276)(174,275)(175,274)(176,273)(177,272)(178,271)(179,270)(180,269)(181,268)(182,267)(183,266)(184,265)(185,264)(186,263)(187,262)(188,261)(189,260)(190,259)(191,258)(192,257)(193,256)(194,255)(195,254)(196,253)(197,252)(198,251)(199,250)(200,249)(201,248)(202,247)(203,246)(204,245)(205,244)(206,243)(207,242)(208,241)(209,240)(210,239)(211,238)(212,237)(213,236)(214,235)(215,234)(216,233)(217,232)(218,231)(219,230)(220,229)(221,228)(222,227)(223,226)(224,225)
Polycyclic presentation:
2^2,439|a^2=b,c^a=c^438
Conjugacy classes & character table
442 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1756, 1);
Finite Group Databasebeta