C₁₉×#2922 #14560779

order	2432
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₉×#2922

Subgroups

	subgroup	G/H
center	C₄²×C₁₉	C₂³
commutator	C₂²	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂³×C₄
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₁₉ ◁ G

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 43 points:

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

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#8187, C₁₉×#8188, C₁₉×#8189, …
maximal normal subgroup of	C₁₉×#8187, C₁₉×#8188, C₁₉×#8189, …
maximal quotient of	C₁₉×#20366, C₄×C₁₉×#408, C₄×C₁₉×#424, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1654);

C19×#2922 #14560779