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Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 292 points:
(2,3,5,9,17)(4,7,13,25,47)(6,11,21,40,33)(8,15,29,43,78)(10,19,36,18,34)(12,23,44,80,86)(14,27,51,92,62)(16,31,58,103,164)(20,38,69,48,87)(22,42,76,73,63)(24,46,84,138,130)(26,49,89,35,64)(28,53,96,155,142)(30,56,95,61,109)(32,60,107,171,233)(37,67,41,74,66)(39,71,121,79,131)(45,82,134,150,111)(50,91,148,88,143)(52,94,153,124,112)(54,98,159,104,166)(55,83,136,65,113)(57,101,161,223,204)(59,105,168,229,175)(68,116,81,132,145)(70,119,93,151,114)(72,122,187,165,227)(75,126,118,90,146)(77,129,128,125,115)(85,140,200,110,176)(97,157,219,212,178)(99,141,202,144,205)(100,158,189,190,179)(102,163,225,246,228)(106,170,231,269,255)(108,173,235,272,238)(117,181,139,198,196)(120,184,156,217,206)(123,188,247,234,271)(127,167,186,137,197)(133,194,209,147,207)(135,195,215,191,180)(149,210,152,213,182)(154,216,193,192,183)(160,222,172,177,239)(162,224,267,260,241)(169,230,185,244,221)(174,237,274,275,280)(199,251,253,208,256)(201,252,248,249,242)(203,254,214,261,245)(211,258,218,263,257)(220,264,262,250,243)(226,268,278,240,276)(232,270,259,281,265)(236,273,279,277,266)(282,283,284,285,286,287,288,289,290,291,292);(1,2,4,8,16,32,61,110,177,240,157,220,235,217,159,221,265,219,181,242,251,188,184,243,252,25,48,88,144,197,187,246,261,202,253,270,233,34,63,111,176,36,66,114,38,70,120,185,42,77,103,165,44,81,133,92,150,212,260,281,237,275,132,31,59,106,134,46,85,141,203,53,97,158,143,56,100,161,146,58,104,167,148,209,257,164,3,6,12,24,5,10,20,39,72,123,189,248,273,263,222,266,274,264,40,73,124,190,244,277,269,49,90,147,208,51,93,152,214,254,247,278,271,64,112,178,239,67,115,138,71,69,118,182,78,130,166,228,82,135,168,151,84,139,199,153,215,262,194,60,108,174,195,9,18,35,65,98,160,223,205,101,162,224,207,105,169,225,210,107,172,227,7,14,28,54,11,22,43,79,13,26,50,47,86,142,204,255,280,272,74,125,191,249,76,128,193,91,149,211,259,94,154,171,234,96,156,218,155,113,179,241,276,116,180,198,122,119,183,200,131,121,186,245,136,196,230,213,140,201,231,216,17,33,62,109,175,238,229,19,37,68,117,21,41,75,127,163,226,267,256,170,232,268,258,173,236,80,15,30,57,102,23,45,83,137,27,52,95,87,29,55,99,89,145,206,126,192,250,279,129)
Conjugacy classes & character table
671 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15455, 2);
Finite Group Databasebeta