C₁₉×#901 #14269653

order	1824
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₁₉×#901

Splittings

Fitting	C₂×C₃×C₈×C₁₉ ⋊ C₂
Hall	C₃×C₁₉ ⋊ #131
Sylow	C₃ ⋊ C₁₉×#131

Subgroups

	subgroup	G/H
center	C₈×C₁₉	C₂×D₃
commutator	C₂×C₃	C₂²×C₄×C₁₉
Frattini	C₄	C₂²×D₃×C₁₉
Fitting	C₂×C₃×C₈×C₁₉	C₂
socle	C₂×C₃×C₁₉	C₂²×C₄
prime radical	C₁₉×#235	C₂
cosocle	C₃×C₄	C₂³×C₁₉
hypercenter	C₂×C₈×C₁₉	D₃
hypocenter	C₃	C₁₉×#131
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₈×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)(23,25,26,31,27,32,33,37)(24,29,30,36,28,34,35,38);(24,28)(29,34)(30,35)(36,38);(21,22)(23,24)(25,29)(26,30)(27,28)(31,36)(32,34)(33,35)(37,38)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1824, 880);

C19×#901 #14269653