C₁₉×#2383 #14560240

order	2432
nilpotency class	2
isoclinism	isoclinic class of #560
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#2383

Subgroups

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

456 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 264 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) = 39
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 39 points:

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

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#2383, C₁₉×#34350, C₄×C₁₉×#560, …
maximal normal subgroup of	C₂×C₁₉×#2383, C₁₉×#34350, C₄×C₁₉×#560, …
maximal quotient of	C₁₉×#13830, C₁₉×#13831, C₁₉×#13833, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1115);