C₁₉×#13670 #18019629

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13669
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13670

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2184
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#131 ◁ C₁₉×#504 ◁ G

278 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 74 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)(21,28)(22,33)(23,37)(24,26)(25,39)(29,51)(30,56)(31,57)(32,50)(34,61)(35,65)(36,43)(38,45)(40,68)(41,67)(42,69)(44,46)(47,49)(48,52)(53,62)(54,76)(55,75)(58,72)(59,63)(64,82)(66,77)(70,74)(71,81)(78,80)(79,83);(20,21)(22,29)(23,38)(24,30)(25,45)(26,47)(27,32)(28,37)(31,39)(33,52)(34,62)(35,66)(36,55)(40,57)(41,72)(42,70)(43,54)(44,58)(46,74)(48,63)(49,67)(50,69)(51,61)(53,60)(56,68)(59,77)(64,83)(65,78)(71,80)(73,79)(75,82)(76,81);(20,22,27,36)(21,29,32,55)(23,34,42,64)(24,43,26,33)(25,35,46,65)(28,48,50,76)(30,54,47,52)(31,53,58,79)(37,63,69,81)(38,62,70,83)(39,60,44,73)(40,71,41,59)(45,66,74,78)(49,75,56,51)(57,80,72,77)(61,67,82,68)

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, 6658);