C₁₉×#3165 #14561022

order	2432
nilpotency class	3
isoclinism	isoclinic class of #3055
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#3165

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₂³×C₁₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9420, C₁₉×#9427, C₁₉×#9434, …
maximal normal subgroup of	C₁₉×#9420, C₁₉×#9427, C₁₉×#9434, …
maximal quotient of	C₁₉×#20800, C₁₉×#21159, C₁₉×#21322, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1897);

C19×#3165 #14561022

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#3165 #14561022