C₁₉×#2379 #14560236

order	2432
nilpotency class	2
isoclinism	isoclinic class of #560
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₁₉×#2379

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

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

normal subgroups only

This group has 520 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)(34,38)(35,36)(37,39);(25,28)(29,31)(33,36)(34,39);(24,25,27,28)(26,29,30,31)(32,33)(34,37)(35,36)(38,39);(24,26)(25,29)(27,30)(28,31)(32,34,35,39)(33,37,36,38)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8910, C₁₉×#8911, C₁₉×#8914, …
maximal normal subgroup of	C₁₉×#8910, C₁₉×#8911, C₁₉×#8914, …
maximal quotient of	C₁₉×#13829, C₁₉×#13831, C₁₉×#13832, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1111);