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Aliases
Splittings
Subgroups
28 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 419 points:
(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)(157,192,193,230)(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)(191,194,228,195)(198,231,232,265)(202,235,236,262)(206,239,240,258)(210,243,244,254)(214,247,248,250)(218,251,252,246)(222,255,256,242)(226,259,260,238)(229,233,263,234)(237,266,267,296)(241,270,271,293)(245,274,275,289)(249,278,279,285)(253,282,283,281)(257,286,287,277)(261,290,291,273)(264,268,294,269)(272,297,298,323)(276,301,302,320)(280,305,306,316)(284,309,310,312)(288,313,314,308)(292,317,318,304)(295,299,321,300)(303,324,325,346)(307,328,329,343)(311,332,333,339)(315,336,337,335)(319,340,341,331)(322,326,344,327)(330,347,348,365)(334,351,352,362)(338,355,356,358)(342,359,360,354)(345,349,363,350)(353,366,367,380)(357,370,371,377)(361,374,375,373)(364,368,378,369)(372,381,382,391)(376,385,386,388)(379,383,389,384)(387,392,393,398)(390,394,396,395)(397,399,400,401)(404,405,406,409,407,410,412,415,408,411,413,416,414,417,418,419);(1,2,5,10,19,32,49,70,95,124,157,194,187,150,117,88,63,42,25,12,3,7,14,23,36,53,74,99,128,161,198,233,224,183,146,113,84,59,38,21,8,16,27,40,57,78,103,132,165,202,237,268,259,220,179,142,109,80,55,34,17,29,44,61,82,107,136,169,206,241,272,299,290,255,216,175,138,105,76,51,30,46,65,86,111,140,173,210,245,276,303,326,317,286,251,212,171,134,101,72,47,67,90,115,144,177,214,249,280,307,330,349,340,313,282,247,208,167,130,97,68,92,119,148,181,218,253,284,311,334,353,368,359,336,309,278,243,204,163,126,93,121,152,185,222,257,288,315,338,357,372,383,374,355,332,305,274,239,200,159,122,154,189,226,261,292,319,342,361,376,387,394,385,370,351,328,301,270,235,196,155,191,229,264,295,322,345,364,379,390,397,399,392,381,366,347,324,297,266,231,192,230,265,296,323,346,365,380,391,398,401,400,396,389,378,363,344,321,294,263,228,190,227,262,293,320,343,362,377,388,395,393,386,375,360,341,318,291,260,225,188,153,186,223,258,289,316,339,358,373,384,382,371,356,337,314,287,256,221,184,151,120,149,182,219,254,285,312,335,354,369,367,352,333,310,283,252,217,180,147,118,91,116,145,178,215,250,281,308,331,350,348,329,306,279,248,213,176,143,114,89,66,87,112,141,174,211,246,277,304,327,325,302,275,244,209,172,139,110,85,64,45,62,83,108,137,170,207,242,273,300,298,271,240,205,168,135,106,81,60,43,28,41,58,79,104,133,166,203,238,269,267,236,201,164,131,102,77,56,39,26,15,24,37,54,75,100,129,162,199,234,232,197,160,127,98,73,52,35,22,13,6,11,20,33,50,71,96,125,158,195,193,156,123,94,69,48,31,18,9,4)(402,403)
Conjugacy classes & character table
832 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12832, 218);
Finite Group Databasebeta