C₁₉×#904 #14269656

order	1824
isoclinism	isoclinic class of #204
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₁₉×#904

Splittings

Fitting	C₂×C₃×C₈×C₁₉ ⋊ C₂
Hall	C₃×C₁₉ ⋊ #135
Sylow	C₃ ⋊ C₁₉×#135

Subgroups

	subgroup	G/H
center	C₄×C₁₉	D₁₂
commutator, cosocle	C₃×C₄	C₂³×C₁₉
Frattini	C₄	C₂²×D₃×C₁₉
Fitting	C₂×C₃×C₈×C₁₉	C₂
socle	C₂×C₃×C₁₉	C₂×D₄
hypercenter	C₂×C₈×C₁₉	D₃
hypocenter	C₃	C₁₉×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×C₈×C₁₉

124 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)(23,26,27,34,28,35,25,32)(24,30,29,33,31,37,36,38);(23,25,28,27)(24,29,31,36)(26,32,35,34)(30,33,37,38);(21,22)(23,24)(25,29)(26,33)(27,36)(28,31)(30,34)(32,37)(35,38)

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, 883);

C19×#904 #14269656