C₁₉×#2084 #14559941

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#2084

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

230 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 108 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)(20,21,22,23)(24,25)(26,31)(27,29)(28,30)(33,36)(37,38);(24,26,28,27)(25,29,30,31)(32,33,34,36)(35,37,39,38);(21,23)(24,27,28,26)(25,29,30,31)(33,37)(35,39)(36,38)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7791, C₁₉×#7793, C₁₉×#7798, …
maximal normal subgroup of	C₁₉×#7791, C₁₉×#7793, C₁₉×#7798, …
maximal quotient of	C₁₉×#10651, C₁₉×#10652, C₁₉×#10654, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 816);