C₁₉×#1918 #14559775

order	2432
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#1918

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22)(24,25)(26,29)(27,28)(30,31)(32,33)(34,36)(35,38)(37,39);(20,22,23,21)(25,28)(29,31);(24,26,27,30)(25,29,28,31)(33,36)(34,39)(37,38)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1918, C₁₉×#21032, C₁₉×#21033, …
maximal normal subgroup of	C₂×C₁₉×#1918, C₁₉×#21032, C₁₉×#21033, …
maximal quotient of	C₁₉×#9533, C₁₉×#9537, C₁₉×#10806, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 650);

C19×#1918 #14559775

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1918 #14559775