C₁₉×#2640 #14560497

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₁₉×#2640

Subgroups

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

500 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 200 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)(24,25,28,31)(26,27,30,29)(34,38)(36,39);(20,21,22,23)(24,26,28,30)(25,29,31,27)(32,33,35,37)(34,36,38,39);(20,21)(22,23)(24,26)(25,29)(27,31)(28,30)(32,34)(33,36)(35,38)(37,39);(24,27,28,29)(25,30,31,26)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#10090, C₁₉×#10092, C₁₉×#10098, …
maximal normal subgroup of	C₁₉×#10090, C₁₉×#10092, C₁₉×#10098, …
maximal quotient of	C₁₉×#14260, C₁₉×#14261, C₁₉×#14273, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1372);