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Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 467 points:
(2,3,5,9,17,33,64)(4,7,13,25,48,90,22)(6,11,21,41,79,146,119)(8,15,29,56,49,92,164)(10,19,37,71,131,65,120)(12,23,44,84,153,86,43)(14,27,52,98,175,216,207)(16,31,60,112,154,256,182)(18,35,67,124,34,66,122)(20,39,75,138,234,162,45)(24,46,87,157,235,197,268)(26,50,94,167,135,121,208)(28,54,101,180,288,376,83)(30,58,108,105,95,169,273)(32,62,116,201,289,393,403)(36,69,127,217,91,163,53)(38,73,134,228,147,247,210)(40,77,142,115,200,165,269)(42,81,148,248,223,123,211)(47,89,160,263,85,155,257)(51,96,171,276,274,266,88)(55,103,183,292,381,380,375)(57,106,99,177,284,209,318)(59,110,191,195,258,366,152)(61,114,198,260,347,312,379)(63,118,205,314,306,368,440)(68,126,215,80,145,245,212)(70,129,220,109,93,166,187)(72,133,226,132,224,125,213)(74,136,230,339,255,159,100)(76,140,237,319,282,113,196)(78,144,243,353,426,364,294)(82,150,251,358,344,267,102)(97,173,280,302,130,222,330)(104,185,295,400,340,427,365)(107,188,181,290,394,373,161)(111,193,303,310,395,450,443)(117,203,313,397,446,448,445)(128,219,326,176,283,327,320)(137,232,341,351,345,308,297)(139,236,346,271,231,214,321)(141,239,349,423,392,420,179)(143,241,265,190,170,275,307)(149,250,357,336,246,355,323)(151,253,361,419,309,270,298)(156,259,367,233,343,374,184)(158,261,348,372,389,264,371)(168,272,238,225,332,218,324)(172,278,383,221,329,199,186)(174,281,387,287,242,352,402)(178,286,369,333,422,328,192)(189,299,293,398,447,331,421)(194,305,406,411,408,244,354)(202,311,252,360,435,414,388)(204,315,285,390,322,415,240)(206,317,413,409,452,463,462)(227,335,229,337,249,356,334)(254,363,438,417,458,386,405)(262,370,432,455,449,442,296)(277,382,384,377,342,325,416)(279,385,410,362,437,460,301)(291,396,451,444,429,418,304)(300,404,401,454,428,433,431)(316,412,391,441,425,457,436)(338,424,359,434,430,378,350)(399,453,456,439,461,459,407)(464,465,466,467);(1,2,4,8,16,32,63,54,102,182,257,365,354,416,382,446,208,163,267,374,442,261,369,404,81,149,144,244,353,136,231,138,235,345,33,65,121,209,319,414,457,116,202,312,394,449,461,313,396,452,108,166,270,21,42,82,151,254,27,53,100,179,287,243,324,276,381,120,90,162,266,373,157,260,299,41,80,77,143,242,73,135,89,161,265,280,386,134,229,338,425,424,219,327,346,430,454,438,434,290,395,247,92,165,222,331,101,181,291,13,26,51,97,174,250,217,200,309,64,119,207,273,379,445,462,188,298,403,39,76,141,37,72,46,88,159,256,364,352,433,349,432,337,127,218,325,417,400,390,358,180,289,146,48,91,129,221,118,206,303,385,448,87,158,262,148,249,114,199,308,393,215,323,311,410,456,106,187,297,19,38,74,137,233,23,45,86,153,255,241,351,305,407,228,336,415,341,428,335,284,389,421,460,259,368,357,69,128,62,117,204,278,384,133,227,295,401,455,60,113,197,288,392,437,201,310,409,56,105,186,9,18,36,70,130,11,22,43,83,152,142,240,193,304,405,440,321,272,378,226,334,371,330,420,155,258,281,35,68,31,61,115,171,277,71,132,225,333,423,126,216,234,344,422,361,436,317,413,453,463,198,286,391,52,99,178,5,10,20,40,78,145,246,110,192,302,367,213,167,271,377,444,263,269,376,84,154,173,17,34,15,30,59,111,194,239,350,237,348,431,67,125,214,322,332,283,388,205,316,398,451,356,177,285,363,439,191,275,380,44,85,156,79,147,58,109,190,301,124,212,320,383,447,211,164,268,375,443,96,172,279,7,14,28,55,104,140,238,185,296,402,387,427,230,340,224,175,282,329,419,292,397,248,98,176,253,362,355,169,274,343,429,183,293,399,29,57,107,189,300,360,326,315,412,122,210,196,307,408,50,95,170,3,6,12,24,47,75,139,103,184,294,366,339,426,458,131,223,318,220,328,418,459,370,441,435,150,252,245,94,168,232,342,236,347,406,66,123,160,264,372,251,359,203,314,411,450,112,195,306,25,49,93)
Conjugacy classes & character table
292 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12964, 3);
Finite Group Databasebeta