C₁₉×#1849 #14559706

order	2432
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#1849

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×C₄⋊C₄
prime radical	C₂³×C₁₉	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1216

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)(21,23)(24,25,28,31,29,32,27,37)(26,33,36,38,34,39,35,30);(24,26,27,35,29,34,28,36)(25,30,31,33,32,38,37,39);(20,21,22,23)(26,34)(30,38)(33,39)(35,36)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7374, C₁₉×#8916, C₁₉×#10524, …
maximal normal subgroup of	C₁₉×#7374, C₁₉×#8916, C₁₉×#10524, …
maximal quotient of	C₁₉×#8808, C₁₉×#8809, C₁₉×#8810, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 581);

C19×#1849 #14559706

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1849 #14559706