C₁₉×#2372 #14560229

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₁₉×#2372

Subgroups

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

560 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 280 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)(20,21,23,22)(25,28)(29,31)(32,33,36,35)(34,38,39,37);(20,22,23,21)(33,35)(37,38);(24,25)(26,29)(27,28)(30,31)(32,34,36,39)(33,37,35,38);(24,26,27,30)(25,29,28,31)(32,35,36,33)(34,38,39,37)

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9439, C₁₉×#9441, C₁₉×#12965, …
maximal normal subgroup of	C₁₉×#9439, C₁₉×#9441, C₁₉×#12965, …
maximal quotient of	C₁₉×#13805, C₁₉×#13816, C₁₉×#13824, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1104);