C₁₉×#1590 #14559447

order	2432
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#1590

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	C₄×D₄
prime radical	C₂×D₄×C₁₉	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

166 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1590, C₁₉×#17886, C₁₉×#17891, …
maximal normal subgroup of	C₂×C₁₉×#1590, C₁₉×#17886, C₁₉×#17891, …
maximal quotient of	C₁₉×#8206, C₁₉×#8207, C₁₉×#8283, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 322);