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Aliases
Splittings
Subgroups
132 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 395 points:
(1,2,5,10,19,32,49,70,95,124,157,194,235,280,329,319,274,231,272,317,357,350,298,249,204,163,126,93,121,152,185,222,263,308,340,291,246,205,168,135,106,81,60,43,28,41,58,79,104,133,166,203,244,289,338,371,381,387,389,385,378,367,356,310,261,216,175,138,105,76,51,30,46,65,86,111,140,173,210,251,296,345,303,258,217,180,147,118,91,116,145,178,215,256,301,349,335,282,233,277,324,362,374,364,322,273,228,187,150,117,88,63,42,25,12,3,7,14,23,36,53,74,99,128,161,198,239,284,333,315,270,229,190,227,268,313,355,347,294,245,200,159,122,154,189,226,267,312,336,287,242,201,164,131,102,77,56,39,26,15,24,37,54,75,100,129,162,199,240,285,334,370,380,383,376,365,325,363,354,306,257,212,171,134,101,72,47,67,90,115,144,177,214,255,300,348,299,254,213,176,143,114,89,66,87,112,141,174,211,252,297,346,331,278,326,366,377,384,375,360,318,269,224,183,146,113,84,59,38,21,8,16,27,40,57,78,103,132,165,202,243,288,337,311,266,225,188,153,186,223,264,309,353,343,290,241,196,155,191,230,271,316,332,283,238,197,160,127,98,73,52,35,22,13,6,11,20,33,50,71,96,125,158,195,236,281,330,369,373,361,323,276,321,359,352,302,253,208,167,130,97,68,92,119,148,181,218,259,304,344,295,250,209,172,139,110,85,64,45,62,83,108,137,170,207,248,293,342,327,368,379,386,388,382,372,358,314,265,220,179,142,109,80,55,34,17,29,44,61,82,107,136,169,206,247,292,341,307,262,221,184,151,120,149,182,219,260,305,351,339,286,237,192,232,275,320,328,279,234,193,156,123,94,69,48,31,18,9,4)(393,395);(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,91)(53,72,73,87)(57,76,77,83)(61,80,81,79)(65,84,85,75)(67,88,89,71)(70,93,94,120)(74,97,98,116)(78,101,102,112)(82,105,106,108)(86,109,110,104)(90,113,114,100)(92,117,118,96)(95,122,123,153)(99,126,127,149)(103,130,131,145)(107,134,135,141)(111,138,139,137)(115,142,143,133)(119,146,147,129)(121,150,151,125)(124,155,156,190)(128,159,160,186)(132,163,164,182)(136,167,168,178)(140,171,172,174)(144,175,176,170)(148,179,180,166)(152,183,184,162)(154,187,188,158)(157,192,193,231)(161,196,197,227)(165,200,201,223)(169,204,205,219)(173,208,209,215)(177,212,213,211)(181,216,217,207)(185,220,221,203)(189,224,225,199)(191,228,229,195)(194,233,234,276)(198,237,238,272)(202,241,242,268)(206,245,246,264)(210,249,250,260)(214,253,254,256)(218,257,258,252)(222,261,262,248)(226,265,266,244)(230,269,270,240)(232,273,274,236)(235,278,279,325)(239,282,283,321)(243,286,287,317)(247,290,291,313)(251,294,295,309)(255,298,299,305)(259,302,303,301)(263,306,307,297)(267,310,311,293)(271,314,315,289)(275,318,319,285)(277,322,323,281)(280,327,328,367)(284,331,332,363)(288,335,336,359)(292,339,340,357)(296,343,344,355)(300,347,348,353)(304,350,345,351)(308,352,341,349)(312,354,337,346)(316,356,333,342)(320,358,329,338)(324,360,361,334)(326,364,365,330)(362,372,373,371)(366,375,376,370)(368,374,378,369)(377,382,383,381)(379,384,385,380)(386,388,389,387)(392,393)(394,395);(390,391)
Conjugacy classes & character table
796 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12448, 223);
Finite Group Databasebeta