C₁₉×#2028 #14559885

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

Aliases

direct product

C₁₉×#2028

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

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

normal subgroups only

This group has 246 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) = 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)(20,21,23,25)(22,26,27,24)(28,29)(30,36)(31,39)(32,35)(33,37)(34,40)(38,43)(41,42);(20,22,23,27)(21,24,25,26)(31,40)(33,42)(34,39)(37,41);(28,30,32,38)(29,33,35,42)(31,41,40,37)(34,43,39,36)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7431, C₁₉×#12210, C₁₉×#12212, …
maximal normal subgroup of	C₁₉×#7431, C₁₉×#12210, C₁₉×#12212, …
maximal quotient of	C₁₉×#10341, C₁₉×#10342, C₁₉×#10345, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 760);