C₁₉×#13428 #18019387

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13357
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13428

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×Q₈	C₂³×C₁₉
prime radical	C₂³×C₁₉	#120
LCS	G ▷ C₂²×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×Q₈×C₁₉ ◁ G

444 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 39
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

589 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6416);