C₁₉×#12437 #18018396

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12436
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12437

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1667
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₁₉×#135	D₄
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

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

normal subgroups only

This group has 214 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)(20,21,28,35)(22,36,42,66)(23,43,46,74)(24,32,48,60)(25,31,47,61)(26,34,27,33)(29,51,56,38)(30,57,59,44)(37,67,70,78)(39,55,71,54)(40,65,41,53)(45,75,50,62)(49,63,76,58)(52,69,79,73)(64,77,81,68)(72,82,83,80);(20,22,25,39,26,40,48,51,28,42,47,71,27,41,24,38)(21,29,32,53,33,54,61,66,35,56,60,65,34,55,31,36)(23,37,49,72,45,69,57,77,46,70,76,83,50,73,44,68)(30,52,62,80,58,78,74,81,59,79,75,82,63,67,43,64);(20,23)(21,30)(22,37)(24,44)(25,49)(26,45)(27,50)(28,46)(29,52)(31,43)(32,62)(33,58)(34,63)(35,59)(36,64)(38,68)(39,72)(40,69)(41,73)(42,70)(47,76)(48,57)(51,77)(53,80)(54,78)(55,67)(56,79)(60,75)(61,74)(65,82)(66,81)(71,83)

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, 5425);