C₁₉×#3167 #14561024

order	2432
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#3167

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₁₉×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

412 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)(22,25)(23,24)(26,27)(29,32)(30,34)(33,35);(21,24)(25,27);(28,29,30,32,31,33,34,35);(20,22,23,26)(21,25,24,27)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9054, C₁₉×#9055, C₁₉×#9717, …
maximal normal subgroup of	C₁₉×#9054, C₁₉×#9055, C₁₉×#9717, …
maximal quotient of	C₁₉×#20816, C₁₉×#21274, C₁₉×#21400, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1899);

C19×#3167 #14561024

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#3167 #14561024