C₁₉×#2057 #14559914

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#2057

Subgroups

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

282 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 116 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) = 2432

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7751, C₁₉×#7752, C₁₉×#7756, …
maximal normal subgroup of	C₁₉×#7751, C₁₉×#7752, C₁₉×#7756, …
maximal quotient of	C₁₉×#10567, C₁₉×#10569, C₁₉×#10573, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 789);