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Dic8119 #44570345
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 380 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);(1,3,2,4)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(29,380)(30,379)(31,378)(32,377)(33,376)(34,375)(35,374)(36,373)(37,372)(38,371)(39,370)(40,369)(41,368)(42,367)(43,366)(44,365)(45,364)(46,363)(47,362)(48,361)(49,360)(50,359)(51,358)(52,357)(53,356)(54,355)(55,354)(56,353)(57,352)(58,351)(59,350)(60,349)(61,348)(62,347)(63,346)(64,345)(65,344)(66,343)(67,342)(68,341)(69,340)(70,339)(71,338)(72,337)(73,336)(74,335)(75,334)(76,333)(77,332)(78,331)(79,330)(80,329)(81,328)(82,327)(83,326)(84,325)(85,324)(86,323)(87,322)(88,321)(89,320)(90,319)(91,318)(92,317)(93,316)(94,315)(95,314)(96,313)(97,312)(98,311)(99,310)(100,309)(101,308)(102,307)(103,306)(104,305)(105,304)(106,303)(107,302)(108,301)(109,300)(110,299)(111,298)(112,297)(113,296)(114,295)(115,294)(116,293)(117,292)(118,291)(119,290)(120,289)(121,288)(122,287)(123,286)(124,285)(125,284)(126,283)(127,282)(128,281)(129,280)(130,279)(131,278)(132,277)(133,276)(134,275)(135,274)(136,273)(137,272)(138,271)(139,270)(140,269)(141,268)(142,267)(143,266)(144,265)(145,264)(146,263)(147,262)(148,261)(149,260)(150,259)(151,258)(152,257)(153,256)(154,255)(155,254)(156,253)(157,252)(158,251)(159,250)(160,249)(161,248)(162,247)(163,246)(164,245)(165,244)(166,243)(167,242)(168,241)(169,240)(170,239)(171,238)(172,237)(173,236)(174,235)(175,234)(176,233)(177,232)(178,231)(179,230)(180,229)(181,228)(182,227)(183,226)(184,225)(185,224)(186,223)(187,222)(188,221)(189,220)(190,219)(191,218)(192,217)(193,216)(194,215)(195,214)(196,213)(197,212)(198,211)(199,210)(200,209)(201,208)(202,207)(203,206)(204,205)
Polycyclic presentation:
2,23,353,2|a^2=d,b^a=b^22,c^a=c^352
Conjugacy classes & character table
8122 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32476, 4);
Finite Group Databasebeta