C₁₉×#1647 #14559504

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#1647

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₁₉
prime radical	C₁₉×#547	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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)(22,24)(23,26)(25,27)(28,29,33,37)(30,38,41,42)(31,36,32,35)(34,40,43,39);(21,24)(22,27)(25,26)(28,30,33,41)(29,34,37,43)(31,40,32,39)(35,42,36,38);(29,35)(31,32)(34,42)(36,37)(38,43)(39,40)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1647, C₁₉×#18503, C₁₉×#18516, …
maximal normal subgroup of	C₂×C₁₉×#1647, C₁₉×#18503, C₁₉×#18516, …
maximal quotient of	C₁₉×#7751, C₁₉×#7752, C₁₉×#7763, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 379);