C₁₉×#2061 #14559918

order	2432
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#2061

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂³×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

230 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 92 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)(20,21,24,26)(22,27,23,25)(28,29,31,35)(30,37,38,33)(32,34,40,36)(39,43,41,42);(20,22,24,23)(21,25,26,27)(28,30,31,38)(29,33,35,37)(32,41,40,39)(34,43,36,42);(20,23,24,22)(21,25,26,27)(29,34)(32,40)(33,42)(35,36)(37,43)(39,41)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7442, C₁₉×#12235, C₁₉×#12237, …
maximal normal subgroup of	C₁₉×#7442, C₁₉×#12235, C₁₉×#12237, …
maximal quotient of	C₁₉×#10568, C₁₉×#10569, C₁₉×#10571, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 793);