C₁₉×#13691 #18019650

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13691
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#13691

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2206
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
prime radical	C₁₉×#2263	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

200 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 83
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 83 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,32)(23,38)(24,43)(25,46)(26,50)(27,33)(28,35)(29,40)(30,45)(31,48)(34,63)(36,67)(37,62)(39,72)(41,71)(42,73)(44,53)(47,61)(49,79)(51,59)(52,76)(54,74)(55,80)(56,68)(57,75)(58,69)(60,66)(64,70)(65,83)(77,78)(81,82);(20,22,24,35,27,37,45,26)(21,28,30,32,33,50,43,62)(23,34,39,64,42,65,41,51)(25,36,44,66,49,69,77,48)(29,52,54,61,57,55,56,82)(31,53,58,46,60,78,67,79)(38,70,71,63,73,59,72,83)(40,47,68,76,75,81,74,80);(20,23)(21,29)(22,34)(24,39)(25,47)(26,51)(27,42)(28,52)(30,54)(31,59)(32,61)(33,57)(35,64)(36,68)(37,65)(38,46)(40,48)(41,45)(43,56)(44,76)(49,81)(50,55)(53,72)(58,83)(60,70)(62,82)(63,67)(66,75)(69,74)(71,78)(73,79)(77,80)

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6679);