C₁₉×#1610 #14559467

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#1610

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₁₉×#537	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

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

normal subgroups only

This group has 254 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) = 608

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)(20,21)(22,24)(23,26)(25,27)(28,29,32,35)(30,33,37,40)(31,34,38,41)(36,42,43,39);(21,24)(22,27)(25,26)(28,30)(29,33)(31,36)(32,37)(34,39)(35,40)(38,43)(41,42);(28,31,32,38)(29,34,35,41)(30,36,37,43)(33,39,40,42)

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12097, C₁₉×#12098, C₁₉×#12099, …
maximal normal subgroup of	C₁₉×#12097, C₁₉×#12098, C₁₉×#12099, …
maximal quotient of	C₁₉×#7790, C₁₉×#7791, C₁₉×#7792, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 342);