C₁₉×#947 #14269699

order	1824
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂×C₄

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₁₉×#947

Splittings

Fitting	C₂×C₃×Q₈×C₁₉ ⋊ C₂
Hall	C₃×C₁₉ ⋊ #124
Sylow	C₃ ⋊ C₁₉×#124

Subgroups

	subgroup	G/H
center	C₂²×C₁₉	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₁₉
Frattini	C₂²	C₂²×D₃×C₁₉
Fitting	C₂×C₃×Q₈×C₁₉	C₂
socle	C₂²×C₃×C₁₉	C₂³
prime radical	C₂×C₁₉×D₁₂	C₂
hypercenter	C₂×Q₈×C₁₉	D₃
hypocenter	C₃	C₁₉×#124
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×Q₈×C₁₉

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 912

A minimal faithful permutation representation — 3 generators on 34 points:

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

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, 926);

C19×#947 #14269699