C₁₉×#2089 #14559946

order	2432
nilpotency class	3
isoclinism	isoclinic class of #2018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#2089

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂³×C₁₉	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

176 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 84 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)(20,21)(22,27)(23,25)(24,26)(28,29,31,36,33,37,32,35)(30,34,39,42,40,41,38,43);(20,22,24,23)(21,25,26,27)(28,30)(29,34)(31,39)(32,38)(33,40)(35,43)(36,42)(37,41);(20,23,24,22)(21,25,26,27)(29,35)(30,38)(31,32)(34,41)(36,37)(39,40)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12294, C₁₉×#12295, C₁₉×#12296, …
maximal normal subgroup of	C₁₉×#12294, C₁₉×#12295, C₁₉×#12296, …
maximal quotient of	C₁₉×#10649, C₁₉×#10650, C₁₉×#10651, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 821);