C₁₉×#8772 #18014731

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8760
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#8772

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#381
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

446 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 114 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)(20,21,23,26,24,22,27,25)(28,29)(30,37,39,33)(31,36)(32,35)(34,38,41,43)(40,42);(28,30)(29,33)(31,38)(32,39)(34,36)(35,37)(40,43)(41,42);(20,22)(21,24)(23,25)(26,27)(28,30)(29,34,35,41)(31,38)(32,39)(33,36,37,42)(40,43)

Conjugacy classes & character table

817 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 1760);