C₁₉×#12065 #18018024

order	4864
nilpotency class	4
isoclinism	isoclinic class of #2180
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12065

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#442
commutator	C₈	C₂²×C₈×C₁₉
Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₂×D₈×C₁₉	C₂×C₄
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₁₉×#322 ◁ G

230 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 2432

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

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5053);