C₁₁⋊(D₅₇₇⋊C₃) #49185199

order	38082
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₁₁⋊(D₅₇₇⋊C₃)
unambiguous semidirect product	(C₅₇₇⋊C₃)⋊D₁₁
unambiguous semidirect product	D₆₃₄₇⋊C₃

Splittings

Fitting, socle, derived, Hall	C₁₁×C₅₇₇ ⋊ C₂×C₃
Hall	C₁₁×C₅₇₇⋊C₃ ⋊ C₂
Hall	D₆₃₄₇ ⋊ C₃
Hall	C₅₇₇⋊C₃ ⋊ D₁₁
Sylow	C₅₇₇ ⋊ C₃×D₁₁
Sylow	C₁₁ ⋊ D₅₇₇⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₅₇₇	C₂×C₃
LCS	G ▷ C₁₁×C₅₇₇
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 588
transitive degree	μ_t(G) = 6347

A minimal faithful permutation representation — 2 generators on 588 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(13,17,18,14,15,19)(16,25,26,20,21,35)(22,38,39,28,29,52)(23,37,33,31,27,24)(30,57,58,41,42,75)(32,55,56,44,40,49)(34,36,54,46,47,50)(43,80,81,60,61,104)(45,78,79,63,59,72)(48,53,77,65,66,73)(51,93,91,69,70,68)(62,109,110,83,84,139)(64,107,108,86,82,101)(67,76,106,88,89,102)(71,122,123,94,95,97)(74,128,120,98,99,92)(85,144,145,112,113,180)(87,142,143,115,111,136)(90,105,141,117,118,137)(96,157,158,124,125,132)(100,164,162,129,130,127)(103,169,155,133,134,121)(114,185,186,147,148,227)(116,183,184,150,146,177)(119,140,182,152,153,178)(126,198,199,159,160,173)(131,205,206,165,166,168)(135,211,203,170,171,163)(138,216,196,174,175,156)(149,232,233,188,189,280)(151,230,231,191,187,224)(154,181,229,193,194,225)(161,245,246,200,201,220)(167,252,253,207,208,215)(172,259,257,212,213,210)(176,264,250,217,218,204)(179,269,243,221,222,197)(190,285,286,235,236,339)(192,283,284,238,234,277)(195,228,282,240,241,278)(202,298,299,247,248,273)(209,305,306,254,255,268)(214,312,313,260,261,263)(219,318,310,265,266,258)(223,323,303,270,271,251)(226,328,296,274,275,244)(237,344,345,288,289,404)(239,342,343,291,287,336)(242,281,341,293,294,337)(249,357,358,300,301,332)(256,364,365,307,308,327)(262,371,372,314,315,322)(267,378,376,319,320,317)(272,383,369,324,325,311)(276,388,362,329,330,304)(279,393,355,333,334,297)(290,409,410,347,348,475)(292,407,408,350,346,401)(295,340,406,352,353,402)(302,422,423,359,360,397)(309,429,430,366,367,392)(316,436,437,373,374,387)(321,443,444,379,380,382)(326,449,441,384,385,377)(331,454,434,389,390,370)(335,459,427,394,395,363)(338,464,420,398,399,356)(349,480,481,412,413,541)(351,478,479,415,411,472)(354,405,477,417,418,473)(361,491,492,424,425,468)(368,498,499,431,432,463)(375,505,506,438,439,458)(381,511,512,445,446,453)(386,516,514,450,451,448)(391,519,509,455,456,442)(396,522,503,460,461,435)(400,525,496,465,466,428)(403,530,489,469,470,421)(414,523,510,462,483,562)(416,544,545,484,482,538)(419,476,543,486,487,539)(426,550,551,493,494,534)(433,555,556,500,501,529)(440,560,561,507,508,524)(447,557,564,502,513,521)(452,552,566,495,517,518)(457,546,565,485,520,515)(467,567,558,526,527,504)(471,568,553,531,532,497)(474,572,548,535,536,490)(488,542,563,528,547,579)(533,585,582,569,570,559)(537,586,580,573,574,554)(540,584,571,576,577,549)(575,587,588,581,578,583);(1,2,4,6,8,10,11,9,7,5,3)(12,13,16,22,30,43,62,85,114,149,190,237,290,349,414,460,394,333,241,148,187,201,208,213,218,222,225,227,277,332,392,458,521,551,479,345,406,464,459,454,449,443,436,429,422,407,344,405,474,537,575,580,553,496,427,362,303,250,203,162,123,79,39,54,55,38,53,74,100,131,167,209,256,309,368,433,502,445,379,319,265,217,174,118,61,82,95,99,102,104,136,173,215,263,317,377,442,510,563,584,586,585,547,413,482,494,501,508,513,517,520,523,527,532,536,539,541,565,514,444,372,306,246,184,110,141,169,164,157,142,109,140,179,223,272,326,386,452,493,424,359,300,247,200,159,124,94,69,47,21,27,35,49,68,92,121,156,197,244,297,356,421,490,549,569,531,469,353,236,287,301,308,315,320,325,330,334,337,339,401,468,529,561,499,423,343,233,282,328,323,318,312,305,298,283,232,281,338,400,467,528,486,417,352,293,240,193,152,117,88,65,46,33,18,17,23,32,45,64,87,116,151,192,239,292,351,416,485,455,389,329,274,194,113,146,160,166,171,175,178,180,224,273,327,387,453,518,545,410,477,530,525,522,519,516,511,505,498,491,478,409,476,540,578,588,582,558,503,434,369,310,257,206,158,108,58,77,93,78,57,76,103,135,172,214,262,316,375,440,507,438,373,314,260,212,170,133,89,42,59,70,73,75,101,132,168,210,258,311,370,435,504,559,583,587,576,487,348,411,425,432,439,446,451,456,461,466,470,473,475,538,566,512,437,365,299,231,145,182,216,211,205,198,183,144,181,226,276,331,391,457,484,415,350,291,238,191,150,115,86,63,44,31,15,19,24,34,48,67,90,119,154,195,242,295,354,419,488,526,465,398,294,189,234,248,255,261,266,271,275,278,280,336,397,463,524,556,492,408,286,341,393,388,383,378,371,364,357,342,285,340,403,471,533,571,548,489,420,355,296,243,196,155,120,91,56,26,37,25,36,51,71,96,126,161,202,249,302,361,426,495,450,384,324,270,221,153,84,111,125,130,134,137,139,177,220,268,322,382,448,515,481,543,572,568,567,483,546,552,557,560,555,550,544,480,542,570,574,577,579,562,509,441,376,313,253,199,143,81,106,128,122,107,80,105,138,176,219,267,321,381,447,500,431,366,307,254,207,165,129,98,66,29,40,50,52,72,97,127,163,204,251,304,363,428,497,554,581,573,535,418,289,346,360,367,374,380,385,390,395,399,402,404,472,534,564,506,430,358,284,186,229,269,264,259,252,245,230,185,228,279,335,396,462,412,347,288,235,188,147,112,83,60,41,28,20,14)

Polycyclic presentation:

2,3,11,577|c^a=c^10,d^a=d^576,d^b=d^363

Conjugacy classes & character table

1077 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38082, 12);

C11⋊(D577⋊C3) #49185199