C₁₉×#13742 #18019701

order	4864
nilpotency class	6
isoclinism	isoclinic class of #13742
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#13742

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×D₃₂
commutator, Frattini, cosocle	C₃₂	C₂³×C₁₉
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×C₈×C₁₉ ◁ C₂×C₁₆×C₁₉ ◁ C₂×C₁₉×C₃₂ ◁ G

134 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 58 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)(22,27)(23,38)(24,42)(25,45)(26,28)(29,33)(30,34)(31,39)(32,43)(35,56)(36,57)(37,46)(40,73)(41,69)(44,75)(47,59)(48,58)(49,66)(50,61)(51,64)(52,72)(53,65)(54,68)(55,74)(60,76)(62,71)(63,70)(67,80)(77,82)(78,81)(79,83);(21,27)(22,33)(23,34)(24,39)(25,43)(28,46)(29,30)(31,56)(32,57)(35,65)(36,68)(37,61)(38,47)(40,74)(41,64)(42,48)(44,72)(45,49)(50,51)(52,80)(53,71)(54,70)(55,76)(58,59)(60,66)(62,63)(67,83)(69,77)(73,79)(75,78)(81,82);(21,28)(27,46)(29,50)(30,51)(31,52)(32,45)(38,69)(42,75)(47,77)(48,78)(49,57)(53,79)(54,76)(55,70)(56,80)(71,73)

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, 6730);