C₁₉×#2091 #14559948

order	2432
nilpotency class	3
isoclinism	isoclinic class of #2010
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#2091

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#127
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂×C₁₉	#399
prime radical	C₂⁴×C₁₉	Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7432, C₁₉×#7433, C₁₉×#12298, …
maximal normal subgroup of	C₁₉×#7432, C₁₉×#7433, C₁₉×#12298, …
maximal quotient of	C₁₉×#10659, C₁₉×#10660, C₁₉×#10661, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 823);

C19×#2091 #14559948

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#2091 #14559948