C₁₉×#876 #14269628

order	1824
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₁₉×#876

Splittings

Fitting	C₃×C₄²×C₁₉ ⋊ C₂
Hall	C₃×C₁₉ ⋊ #126
Sylow	C₃ ⋊ C₁₉×#126

Subgroups

	subgroup	G/H
center	C₂²×C₁₉	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₁₉
Frattini	C₂²	C₂²×D₃×C₁₉
Fitting	C₃×C₄²×C₁₉	C₂
socle	C₂²×C₃×C₁₉	C₂³
prime radical	C₂²×D₃×C₁₉	C₂²
hypercenter	C₄²×C₁₉	D₃
hypocenter	C₃	C₁₉×#126
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 912

A minimal faithful permutation representation — 3 generators on 38 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22)(24,28)(27,30)(31,33,34,38)(32,36,35,37);(23,25,26,29)(24,27,28,30)(32,35)(36,37);(21,22)(23,24)(25,27)(26,28)(29,30)(31,32)(33,37)(34,35)(36,38)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1824, 855);

C19×#876 #14269628