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Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 384 points:
(2,3,5,9,17,33,64)(4,7,13,25,49,96,175)(6,11,21,41,80,44,86)(8,15,29,57,112,205,73)(10,19,37,72,135,65,123)(12,23,45,88,95,173,271)(14,27,53,104,189,289,158)(16,31,60,26,51,100,30)(18,35,68,128,34,66,124)(20,39,76,141,236,176,256)(22,43,84,154,232,87,159)(24,47,92,168,264,343,136)(28,55,108,197,301,364,348)(32,62,119,89,162,253,146)(36,70,131,219,97,105,191)(38,74,137,231,147,91,166)(40,78,144,239,196,299,138)(42,82,150,157,229,125,218)(46,90,164,257,186,285,252)(48,94,171,142,71,133,59)(50,98,178,276,67,126,140)(52,102,185,145,221,274,342)(54,106,193,226,118,160,117)(56,110,201,307,368,250,230)(58,114,208,317,182,61,79)(63,121,179,198,303,149,242)(69,129,222,81,148,107,195)(75,139,233,331,174,272,292)(77,143,237,333,290,320,261)(83,152,245,297,332,192,293)(85,156,249,336,330,167,262)(93,134,227,170,235,101,183)(99,180,277,268,177,194,296)(103,187,286,287,351,363,234)(109,199,305,217,322,356,211)(111,203,310,284,115,210,116)(113,206,314,155,127,220,251)(120,188,169,266,344,347,280)(122,216,281,172,247,240,181)(130,223,283,161,204,312,352)(132,207,315,190,258,275,298)(151,243,260,329,241,200,306)(153,246,325,214,300,269,238)(163,255,339,335,323,294,358)(165,259,340,319,212,263,213)(184,282,202,279,273,349,361)(209,316,373,295,326,270,337)(215,278,308,369,291,341,353)(224,324,362,265,304,367,248)(225,318,374,302,365,350,377)(228,327,309,355,254,338,288)(244,334,328,376,313,372,366)(267,346,321,354,311,359,357)(345,370,379,360,375,371,378)(380,381,382,383,384);(1,2,4,8,16,32,63,122,217,39,77,49,97,177,275,351,141,92,169,267,293,150,51,101,184,283,355,74,138,232,330,277,344,303,366,57,113,207,316,312,84,155,248,55,109,200,307,364,231,329,233,119,213,320,189,290,90,165,260,342,148,241,327,375,314,368,70,132,225,108,198,304,343,154,144,240,223,315,272,82,151,244,47,93,170,268,5,10,20,40,79,146,88,161,64,86,158,100,182,280,353,346,237,171,269,236,332,245,106,194,297,362,378,143,238,220,317,216,321,33,65,31,61,118,212,3,6,12,24,48,95,174,273,350,78,145,98,179,9,18,36,71,134,228,328,358,243,102,186,104,190,291,139,234,239,201,308,370,367,249,114,209,318,374,372,156,250,336,110,202,309,369,13,26,52,103,188,288,164,258,124,166,261,185,284,242,331,376,175,271,348,133,226,325,199,17,34,67,127,221,323,324,373,349,152,68,112,94,172,270,347,11,22,44,87,160,253,162,254,123,159,252,183,281,21,42,83,153,247,335,168,265,128,195,298,193,295,360,96,176,274,310,322,333,66,125,62,120,214,301,7,14,28,56,111,204,313,72,29,58,115,180,278,19,38,75,140,235,257,286,357,334,187,287,191,292,25,50,99,181,279,37,73,136,230,210,319,197,302,135,229,131,208,203,311,371,379,27,54,107,196,300,339,259,341,218,262,289,285,356,45,89,163,256,80,147,227,326,222,306,35,69,130,224,178,264,276,352,377,246,129,206,173,41,81,149,23,46,91,167,263,338,255,137,60,117,211,282,354,43,85,157,251,337,340,266,345,205,299,363,296,361,53,105,192,294,359,76,142,126,219,121,215,305,365,15,30,59,116)
Conjugacy classes & character table
305 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13265, 1);
Finite Group Databasebeta