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Dic4537 #31827504
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 366 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);(1,3,2,4)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)(19,366)(20,365)(21,364)(22,363)(23,362)(24,361)(25,360)(26,359)(27,358)(28,357)(29,356)(30,355)(31,354)(32,353)(33,352)(34,351)(35,350)(36,349)(37,348)(38,347)(39,346)(40,345)(41,344)(42,343)(43,342)(44,341)(45,340)(46,339)(47,338)(48,337)(49,336)(50,335)(51,334)(52,333)(53,332)(54,331)(55,330)(56,329)(57,328)(58,327)(59,326)(60,325)(61,324)(62,323)(63,322)(64,321)(65,320)(66,319)(67,318)(68,317)(69,316)(70,315)(71,314)(72,313)(73,312)(74,311)(75,310)(76,309)(77,308)(78,307)(79,306)(80,305)(81,304)(82,303)(83,302)(84,301)(85,300)(86,299)(87,298)(88,297)(89,296)(90,295)(91,294)(92,293)(93,292)(94,291)(95,290)(96,289)(97,288)(98,287)(99,286)(100,285)(101,284)(102,283)(103,282)(104,281)(105,280)(106,279)(107,278)(108,277)(109,276)(110,275)(111,274)(112,273)(113,272)(114,271)(115,270)(116,269)(117,268)(118,267)(119,266)(120,265)(121,264)(122,263)(123,262)(124,261)(125,260)(126,259)(127,258)(128,257)(129,256)(130,255)(131,254)(132,253)(133,252)(134,251)(135,250)(136,249)(137,248)(138,247)(139,246)(140,245)(141,244)(142,243)(143,242)(144,241)(145,240)(146,239)(147,238)(148,237)(149,236)(150,235)(151,234)(152,233)(153,232)(154,231)(155,230)(156,229)(157,228)(158,227)(159,226)(160,225)(161,224)(162,223)(163,222)(164,221)(165,220)(166,219)(167,218)(168,217)(169,216)(170,215)(171,214)(172,213)(173,212)(174,211)(175,210)(176,209)(177,208)(178,207)(179,206)(180,205)(181,204)(182,203)(183,202)(184,201)(185,200)(186,199)(187,198)(188,197)(189,196)(190,195)(191,194)(192,193)
Polycyclic presentation:
2,13,349,2|a^2=d,b^a=b^12,c^a=c^348
Conjugacy classes & character table
4540 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18148, 4);
Finite Group Databasebeta