C₁₉×#8491 #18014450

order	4864
nilpotency class	3
isoclinism	isoclinic class of #8491
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₉×#8491

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3549	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

820 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 820 conjugacy classes of subgroups — too many to draw. Only its 142 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)(21,24,25,26)(28,29)(30,37,39,33)(31,36)(32,35)(34,38,42,40)(41,43);(20,21)(22,26)(23,25)(24,27)(28,30)(29,33)(31,38)(32,39)(34,36)(35,37)(40,41)(42,43);(22,27)(24,26)(28,30)(29,34)(31,40)(32,39)(33,36)(35,42)(37,43)(38,41)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 1479);