C₁₉×#13376 #18019335

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13343
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13376

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×D₄	C₂³×C₁₉
prime radical	C₂×C₁₉×H(5,𝔽₂)	C₂²
LCS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×D₄×C₁₉ ◁ G

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

normal subgroups only

This group has 640 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) = 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)(20,21,23,25)(22,26,27,24)(28,29,32,35)(30,36,38,43)(31,34,39,42)(33,40,41,37);(20,22,23,27)(21,24,25,26)(31,39)(34,42);(28,30)(29,33)(31,37)(32,38)(34,36)(35,41)(39,40)(42,43)

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, 6364);