C₁₉×#1726 #14559583

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₄³×C₁₉ · Schur multiplier (H₂) = C₂×C₄²

Aliases

direct product

C₁₉×#1726

Subgroups

	subgroup	G/H
center	C₂²×C₈×C₁₉	C₂²
commutator	C₂	C₄³×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle, prime radical	C₂³×C₁₉	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₉ ◁ G

328 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(28,29,31,34,32,35,38,41)(30,33,37,40,36,39,42,43);(20,21,22,23)(28,30)(29,33)(31,37)(32,36)(34,40)(35,39)(38,42)(41,43);(24,25,26,27)(30,36)(33,39)(37,42)(40,43)

Conjugacy classes & character table

1520 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#7150, C₁₉×#8137, C₁₉×#8138, …
maximal normal subgroup of	C₁₉×#7150, C₁₉×#8137, C₁₉×#8138, …
maximal quotient of	C₈×C₁₉×#97, C₁₉×#7841, C₁₉×#7842, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 458);

C19×#1726 #14559583