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Aliases
Splittings
Subgroups
54 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 371 points:
(2,4)(3,7)(5,10)(6,13)(8,16)(9,15)(11,20)(12,23)(14,25)(17,29)(18,28)(19,27)(21,34)(22,37)(24,39)(26,41)(30,46)(31,45)(32,44)(33,43)(35,52)(36,55)(38,57)(40,59)(42,61)(47,67)(48,66)(49,65)(50,64)(51,63)(53,74)(54,77)(56,79)(58,81)(60,83)(62,85)(68,92)(69,91)(70,90)(71,89)(72,88)(73,87)(75,100)(76,103)(78,105)(80,107)(82,109)(84,111)(86,113)(93,121)(94,120)(95,119)(96,118)(97,117)(98,116)(99,115)(101,130)(102,133)(104,135)(106,137)(108,139)(110,141)(112,143)(114,145)(122,154)(123,153)(124,152)(125,151)(126,150)(127,149)(128,148)(129,147)(131,164)(132,167)(134,169)(136,171)(138,173)(140,175)(142,177)(144,179)(146,181)(155,191)(156,190)(157,189)(158,188)(159,187)(160,186)(161,185)(162,184)(163,183)(165,200)(166,202)(168,204)(170,206)(172,208)(174,210)(176,212)(178,214)(180,216)(182,218)(192,219)(193,226)(194,225)(195,224)(196,223)(197,222)(198,221)(199,220)(201,234)(203,236)(205,238)(207,240)(209,242)(211,244)(213,246)(215,248)(217,250)(227,251)(228,257)(229,256)(230,255)(231,254)(232,253)(233,252)(235,264)(237,266)(239,268)(241,270)(243,272)(245,274)(247,276)(249,278)(258,279)(259,284)(260,283)(261,282)(262,281)(263,280)(265,290)(267,292)(269,294)(271,296)(273,298)(275,300)(277,302)(285,303)(286,307)(287,306)(288,305)(289,304)(291,312)(293,314)(295,316)(297,318)(299,320)(301,322)(308,323)(309,326)(310,325)(311,324)(313,330)(315,332)(317,334)(319,336)(321,338)(327,339)(328,341)(329,340)(331,344)(333,346)(335,348)(337,350)(342,351)(343,352)(345,354)(347,356)(349,358)(353,359)(355,360)(357,361)(362,365,364,363)(369,370,371);(1,6,24,58,108,174,243,297,335,357,356,334,296,242,173,107,57,23,4,3,14,40,82,140,211,273,319,349,360,346,316,270,208,137,79,37,10,9,8,26,60,110,176,245,299,337,359,354,332,294,240,171,105,55,20,19,18,17,42,84,142,213,275,321,351,352,344,314,268,206,135,77,34,33,32,31,30,62,112,178,247,301,339,341,340,330,292,238,169,103,52,51,50,49,48,47,86,144,215,277,323,326,325,324,312,266,204,133,74,73,72,71,70,69,68,114,180,249,303,307,306,305,304,290,236,167,100,99,98,97,96,95,94,93,146,217,279,284,283,282,281,280,264,202,130,129,128,127,126,125,124,123,122,182,251,257,256,255,254,253,252,234,164,163,162,161,160,159,158,157,156,155,219,226,225,224,223,222,221,220,200,165,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,131,201,233,232,231,230,229,228,227,218,154,153,152,151,150,149,148,147,101,166,235,263,262,261,260,259,258,250,181,121,120,119,118,117,116,115,75,132,203,265,289,288,287,286,285,278,216,145,92,91,90,89,88,87,53,102,168,237,291,311,310,309,308,302,248,179,113,67,66,65,64,63,35,76,134,205,267,313,329,328,327,322,276,214,143,85,46,45,44,43,21,54,104,170,239,293,331,343,342,338,300,246,177,111,61,29,28,27,11,36,78,136,207,269,315,345,353,350,320,274,212,141,83,41,16,15,5,22,56,106,172,241,295,333,355,358,336,298,244,175,109,59,25,7,2,12,38,80,138,209,271,317,347,361,348,318,272,210,139,81,39,13)(366,367,368)
Conjugacy classes & character table
3276 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12996, 23);
Finite Group Databasebeta