C₁₉×D₁₀₁ #16838623

order	3838
isoclinism	isoclinic class of D₁₀₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×D₁₀₁
unambiguous semidirect product	C₁₀₁⋊(C₂×C₁₉)

Splittings

Fitting, socle, Hall	C₁₉×C₁₀₁ ⋊ C₂
derived, Sylow	C₁₀₁ ⋊ C₂×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	D₁₀₁
commutator, cosocle, hypocenter	C₁₀₁	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₉×C₁₀₁	C₂
LCS	G ▷ C₁₀₁
UCS	C₁ ◁ C₁₉

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 120
transitive degree	μ_t(G) = 1919

A minimal faithful permutation representation — 2 generators on 120 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120);(21,120)(22,119)(23,118)(24,117)(25,116)(26,115)(27,114)(28,113)(29,112)(30,111)(31,110)(32,109)(33,108)(34,107)(35,106)(36,105)(37,104)(38,103)(39,102)(40,101)(41,100)(42,99)(43,98)(44,97)(45,96)(46,95)(47,94)(48,93)(49,92)(50,91)(51,90)(52,89)(53,88)(54,87)(55,86)(56,85)(57,84)(58,83)(59,82)(60,81)(61,80)(62,79)(63,78)(64,77)(65,76)(66,75)(67,74)(68,73)(69,72)(70,71)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₁₉×D₁₀₁, C₁₉×D₃₀₃, C₁₉⋊C₃×D₁₀₁, …
maximal normal subgroup of	C₃×C₁₉×D₁₀₁, C₁₉⋊C₃×D₁₀₁, C₅×C₁₉×D₁₀₁, …
maximal quotient of	C₃×C₁₉×D₁₀₁, C₁₉×D₃₀₃, C₅×C₁₉×D₁₀₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3838, 2);

C19×D101 #16838623