C₁₉×#890 #14269643

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

Aliases

direct product

C₁₉×#890

Splittings

Hall	C₃×C₁₉ ⋊ #125
Sylow	C₃ ⋊ C₁₉×#125

Subgroups

	subgroup	G/H
center	C₂²×C₁₉	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₁₉
Frattini	C₂²	C₂²×D₃×C₁₉
Fitting	C₃×C₄⋊C₄×C₁₉	C₂
socle, prime radical	C₂²×C₃×C₁₉	C₂³
hypercenter	C₄⋊C₄×C₁₉	D₃
hypocenter	C₃	C₁₉×#125
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄⋊C₄×C₁₉

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 1824

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)(25,29)(31,33,34,38)(32,35,36,37);(23,25,26,29)(24,27,28,30);(21,22)(23,24)(25,27)(26,28)(29,30)(31,32,34,36)(33,37,38,35)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1824, 870);

C19×#890 #14269643