C₁₉×#936 #14269687

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

Aliases

direct product

C₁₉×#936

Splittings

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, prime radical	C₂×C₃×D₄×C₁₉	C₂
socle	C₂²×C₃×C₁₉	C₂³
hypercenter	C₂×D₄×C₁₉	D₃
hypocenter	C₃	C₁₉×#124
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×D₄×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)(28,32)(29,33);(27,29,30,33)(28,31,32,34);(21,22)(23,24,25,26)(27,28)(29,31)(30,32)(33,34)

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, 914);

C19×#936 #14269687