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Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 548 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21,23,26,30,35,41,48,56,65,75,86,98,111,125,140,156,173,191,210,230,251,273,22,24,27,31,36,42,49,57,66,76,87,99,112,126,141,157,174,192,211,231,252,274,296,25,28,32,37,43,50,58,67,77,88,100,113,127,142,158,175,193,212,232,253,275,297,318,29,33,38,44,51,59,68,78,89,101,114,128,143,159,176,194,213,233,254,276,298,319,339,34,39,45,52,60,69,79,90,102,115,129,144,160,177,195,214,234,255,277,299,320,340,359,40,46,53,61,70,80,91,103,116,130,145,161,178,196,215,235,256,278,300,321,341,360,378,47,54,62,71,81,92,104,117,131,146,162,179,197,216,236,257,279,301,322,342,361,379,396,55,63,72,82,93,105,118,132,147,163,180,198,217,237,258,280,302,323,343,362,380,397,413,64,73,83,94,106,119,133,148,164,181,199,218,238,259,281,303,324,344,363,381,398,414,429,74,84,95,107,120,134,149,165,182,200,219,239,260,282,304,325,345,364,382,399,415,430,444,85,96,108,121,135,150,166,183,201,220,240,261,283,305,326,346,365,383,400,416,431,445,458,97,109,122,136,151,167,184,202,221,241,262,284,306,327,347,366,384,401,417,432,446,459,471,110,123,137,152,168,185,203,222,242,263,285,307,328,348,367,385,402,418,433,447,460,472,483,124,138,153,169,186,204,223,243,264,286,308,329,349,368,386,403,419,434,448,461,473,484,494,139,154,170,187,205,224,244,265,287,309,330,350,369,387,404,420,435,449,462,474,485,495,504,155,171,188,206,225,245,266,288,310,331,351,370,388,405,421,436,450,463,475,486,496,505,513,172,189,207,226,246,267,289,311,332,352,371,389,406,422,437,451,464,476,487,497,506,514,521,190,208,227,247,268,290,312,333,353,372,390,407,423,438,452,465,477,488,498,507,515,522,528,209,228,248,269,291,313,334,354,373,391,408,424,439,453,466,478,489,499,508,516,523,529,534,229,249,270,292,314,335,355,374,392,409,425,440,454,467,479,490,500,509,517,524,530,535,539,250,271,293,315,336,356,375,393,410,426,441,455,468,480,491,501,510,518,525,531,536,540,543,272,294,316,337,357,376,394,411,427,442,456,469,481,492,502,511,519,526,532,537,541,544,546,295,317,338,358,377,395,412,428,443,457,470,482,493,503,512,520,527,533,538,542,545,547,548);(1,2,4,6,8,10,12,14,16,18,19,17,15,13,11,9,7,5,3)
Conjugacy classes & character table
5819 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20102, 2);
Finite Group Databasebeta