C₁₉×#948 #14269700

order	1824
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#948

Splittings

Hall	C₃×C₁₉ ⋊ #131
Sylow	C₃ ⋊ C₁₉×#131

Subgroups

	subgroup	G/H
center	C₄×C₁₉	C₂²×D₃
commutator	C₂×C₃	C₂²×C₄×C₁₉
Frattini	C₄	C₂²×D₃×C₁₉
Fitting, prime radical	C₃×#41×C₁₉	C₂
socle	C₂×C₃×C₁₉	C₂²×C₄
cosocle	C₃×C₄	C₂³×C₁₉
hypercenter	#41×C₁₉	D₃
hypocenter	C₃	C₁₉×#131
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₁₉ ◁ #41×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)(25,31)(28,34)(32,37)(35,38);(23,25)(24,28)(26,32)(27,31)(29,35)(30,34)(33,37)(36,38);(21,22)(23,24,26,29,27,30,33,36)(25,28,32,35,31,34,37,38)

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, 927);

C19×#948 #14269700