C₂×D₁₁×C₅₂₉ #37551722

order	23276
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₁₁×C₅₂₉
unambiguous semidirect product	C₁₁⋊(C₂²×C₅₂₉)
unambiguous semidirect product	(C₂×C₁₁)⋊(C₂×C₅₂₉)

Splittings

Fitting	C₂×C₁₁×C₅₂₉ ⋊ C₂
derived, Sylow	C₁₁ ⋊ C₂²×C₅₂₉
Hall	C₁₁×C₅₂₉ ⋊ C₂²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅₂₉	D₁₁
commutator, hypocenter	C₁₁	C₂²×C₅₂₉
Frattini	C₂₃	C₂×D₁₁×C₂₃
Fitting	C₂×C₁₁×C₅₂₉	C₂
socle	C₂×C₁₁×C₂₃	C₂×C₂₃
prime radical	C₂×D₁₁×C₂₃	C₂₃
cosocle	C₁₁×C₂₃	C₂²×C₂₃
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₅₂₉

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 542
transitive degree	μ_t(G) = 11638

A minimal faithful permutation representation — 2 generators on 542 points:

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

Conjugacy classes & character table

7406 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23276, 12);

C2×D11×C529 #37551722