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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 394 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);(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)(23,394)(24,393)(25,392)(26,391)(27,390)(28,389)(29,388)(30,387)(31,386)(32,385)(33,384)(34,383)(35,382)(36,381)(37,380)(38,379)(39,378)(40,377)(41,376)(42,375)(43,374)(44,373)(45,372)(46,371)(47,370)(48,369)(49,368)(50,367)(51,366)(52,365)(53,364)(54,363)(55,362)(56,361)(57,360)(58,359)(59,358)(60,357)(61,356)(62,355)(63,354)(64,353)(65,352)(66,351)(67,350)(68,349)(69,348)(70,347)(71,346)(72,345)(73,344)(74,343)(75,342)(76,341)(77,340)(78,339)(79,338)(80,337)(81,336)(82,335)(83,334)(84,333)(85,332)(86,331)(87,330)(88,329)(89,328)(90,327)(91,326)(92,325)(93,324)(94,323)(95,322)(96,321)(97,320)(98,319)(99,318)(100,317)(101,316)(102,315)(103,314)(104,313)(105,312)(106,311)(107,310)(108,309)(109,308)(110,307)(111,306)(112,305)(113,304)(114,303)(115,302)(116,301)(117,300)(118,299)(119,298)(120,297)(121,296)(122,295)(123,294)(124,293)(125,292)(126,291)(127,290)(128,289)(129,288)(130,287)(131,286)(132,285)(133,284)(134,283)(135,282)(136,281)(137,280)(138,279)(139,278)(140,277)(141,276)(142,275)(143,274)(144,273)(145,272)(146,271)(147,270)(148,269)(149,268)(150,267)(151,266)(152,265)(153,264)(154,263)(155,262)(156,261)(157,260)(158,259)(159,258)(160,257)(161,256)(162,255)(163,254)(164,253)(165,252)(166,251)(167,250)(168,249)(169,248)(170,247)(171,246)(172,245)(173,244)(174,243)(175,242)(176,241)(177,240)(178,239)(179,238)(180,237)(181,236)(182,235)(183,234)(184,233)(185,232)(186,231)(187,230)(188,229)(189,228)(190,227)(191,226)(192,225)(193,224)(194,223)(195,222)(196,221)(197,220)(198,219)(199,218)(200,217)(201,216)(202,215)(203,214)(204,213)(205,212)(206,211)(207,210)(208,209)
Conjugacy classes & character table
7090 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28348, 11);
Finite Group Databasebeta