C₁₉×#1450 #14559307

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈×C₁₉ · Schur multiplier (H₂) = C₂×C₈

Aliases

direct product

C₁₉×#1450

Subgroups

	subgroup	G/H
center	C₄×C₈×C₁₉	C₂²
commutator	C₂	C₂×C₄×C₈×C₁₉
Frattini, cosocle	C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×C₄²
prime radical	C₂³×C₁₉	C₄²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₁₉ ◁ G

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1216

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);(20,21,22,24,23,25,26,27)(28,30)(29,33)(31,37)(32,36)(34,40)(35,39)(38,42)(41,43);(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×#7140, C₁₉×#7141, C₁₉×#7153, …
maximal normal subgroup of	C₁₉×#7140, C₁₉×#7141, C₁₉×#7153, …
maximal quotient of	C₁₉×#7841, C₁₉×#7849, C₁₉×#8133, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 182);

C19×#1450 #14559307