C₁₉×#2983 #14560840

order	2432
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#2983

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂³×C₄
prime radical	C₂³×C₁₉	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

356 conjugacy classes of subgroups; only the 268 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 268 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 — 4 generators on 43 points:

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8838, C₁₉×#8865, C₁₉×#8962, …
maximal normal subgroup of	C₁₉×#8838, C₁₉×#8865, C₁₉×#8962, …
maximal quotient of	C₁₉×#20534, C₁₉×#20536, C₁₉×#20570, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1715);