C₁₉×#828 #14268981

order	1824
isoclinism	isoclinic class of #826
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₉×#828

Splittings

Fitting	C₃×Q₁₆×C₁₉ ⋊ C₂
Hall	C₃×C₁₉ ⋊ SD₃₂
Sylow	C₃ ⋊ C₁₉×SD₃₂

Subgroups

	subgroup	G/H
center	C₂×C₁₉	#213
commutator, cosocle	C₃×C₈	C₂²×C₁₉
Frattini	C₈	C₂×D₃×C₁₉
Fitting	C₃×Q₁₆×C₁₉	C₂
socle	C₂×C₃×C₁₉	D₈
prime radical	C₁₉×D₂₄	C₂
hypercenter	Q₁₆×C₁₉	D₃
hypocenter	C₃	C₁₉×SD₃₂
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₉ ◁ C₄×C₁₉ ◁ C₈×C₁₉ ◁ Q₁₆×C₁₉

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 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)(23,24,27,30)(25,32,34,38)(26,35,33,29)(28,36,37,31);(21,22)(24,28)(25,31)(26,33)(29,38)(30,37)(32,35)(34,36)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1824, 208);

C19×#828 #14268981