C₁₉×C₂₈₃⋊C₃ #30633199

order	16131
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×C₂₈₃⋊C₃
unambiguous semidirect product	C₂₈₃⋊(C₃×C₁₉)

Splittings

Fitting, socle, Hall	C₁₉×C₂₈₃ ⋊ C₃
derived, Sylow	C₂₈₃ ⋊ C₃×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	C₂₈₃⋊C₃
commutator, cosocle, hypocenter	C₂₈₃	C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₉×C₂₈₃	C₃
LCS	G ▷ C₂₈₃
UCS	C₁ ◁ C₁₉

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 302
transitive degree	μ_t(G) = 5377

A minimal faithful permutation representation — 2 generators on 302 points:

(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,70)(41,56,67)(44,59,64)(47,62,61)(50,65,58)(52,68,55)(54,72,92)(57,75,89)(60,78,86)(63,81,83)(66,84,80)(69,87,77)(71,90,74)(73,94,117)(76,97,114)(79,100,111)(82,103,108)(85,106,105)(88,109,102)(91,112,99)(93,115,96)(95,119,145)(98,122,142)(101,125,139)(104,128,136)(107,131,133)(110,134,130)(113,137,127)(116,140,124)(118,143,121)(120,147,175)(123,150,172)(126,148,169)(129,155,166)(132,158,163)(135,161,160)(138,164,157)(141,167,154)(144,170,152)(146,173,149)(151,178,202)(153,179,199)(156,183,196)(159,185,193)(162,188,190)(165,191,187)(168,194,184)(171,197,182)(174,200,180)(176,203,177)(181,206,224)(186,209,219)(189,211,216)(192,214,213)(195,217,210)(198,220,208)(201,222,207)(204,225,205)(212,230,237)(215,232,234)(218,235,231)(221,238,229)(223,240,228)(226,242,227)(233,247,251)(236,249,248)(239,252,246)(241,254,245)(243,256,244)(250,261,262)(253,263,260)(255,265,259)(257,267,258)(264,272,271)(266,273,270)(268,275,269)(274,279,278)(276,280,277)(281,283,282)(284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302);(1,2,4,8,15,25,38,54,73,95,120,148,97,53,71,91,113,138,165,192,215,233,242,200,143,92,114,139,166,193,216,234,248,260,270,277,279,263,235,191,134,84,46,20,5,9,16,26,39,55,74,96,121,149,177,183,125,75,37,52,69,88,110,135,162,189,212,225,173,117,142,169,196,219,237,251,262,271,278,282,283,273,252,217,164,109,65,33,12,19,29,42,58,77,99,124,152,180,205,209,155,100,56,24,36,50,66,85,107,132,159,186,203,145,172,199,147,176,204,226,243,257,268,276,281,280,265,238,194,137,87,49,22,32,45,61,80,102,127,154,182,207,227,230,185,128,78,40,14,23,34,47,63,82,104,129,156,175,202,224,178,119,146,174,201,223,241,255,266,274,275,254,220,167,112,68,35,48,64,83,105,130,157,184,208,228,244,247,211,158,103,59,27,7,13,21,31,44,60,79,101,126,153,181,206,150,94,118,144,171,198,221,239,253,264,267,240,197,140,90,51,67,86,108,133,160,187,210,229,245,258,261,232,188,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,179,122,72,93,116,141,168,195,218,236,250,256,222,170,115,70,89,111,136,163,190,213,231,246,259,269,272,249,214,161,106,62,30,10)

Conjugacy classes & character table

1843 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₉×C₂₈₃⋊C₃, C₁₉×D₂₈₃⋊C₃, D₁₉×C₂₈₃⋊C₃, …
maximal normal subgroup of	C₂×C₁₉×C₂₈₃⋊C₃, C₁₉×D₂₈₃⋊C₃, D₁₉×C₂₈₃⋊C₃, …
maximal quotient of	C₂×C₁₉×C₂₈₃⋊C₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16131, 2);

C19×C283⋊C3 #30633199