C₁₉×#1678 #14559535

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1665
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#1678

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₁₉
prime radical	C₁₉×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

160 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 43
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(22,26)(25,27)(28,29)(30,36)(31,33)(32,40)(34,38)(35,39)(37,43)(41,42);(20,21,22,24,23,25,26,27)(29,33)(34,42)(35,40)(36,43);(28,30,31,37)(29,34,33,42)(32,41,39,38)(35,43,40,36)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1678, C₁₉×#19123, C₁₉×#19124, …
maximal normal subgroup of	C₂×C₁₉×#1678, C₁₉×#19123, C₁₉×#19124, …
maximal quotient of	C₁₉×#8647, C₁₉×#9216, C₁₉×#9222, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 410);