C₁₉×#12168 #18018127

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12108
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#12168

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂³×C₁₉	AGL(1,ℤ/8)
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#424 ◁ G

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

normal subgroups only

This group has 330 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) = 91
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 91 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,27)(28,29,35,41)(30,42,46,70)(31,47,50,67)(32,51,55,65)(33,40,34,39)(36,58,61,44)(37,56,63,49)(38,53,66,54)(43,71,75,88)(45,76,57,64)(48,79,82,62)(52,68,83,60)(59,80,87,91)(69,74,90,73)(72,77,85,86)(78,84,89,81);(20,21)(22,24)(23,25)(26,27)(28,30,35,46)(29,36,41,61)(31,43,50,75)(32,52,55,83)(33,45,34,57)(37,59,63,87)(38,64,66,76)(39,60,40,68)(42,65,70,51)(44,53,58,54)(47,77,67,86)(48,80,82,91)(49,73,56,74)(62,88,79,71)(69,89,90,78)(72,84,85,81);(20,22,23,26)(21,24,25,27)(28,31)(29,37)(30,43)(32,48)(33,56)(34,49)(35,50)(36,59)(38,62)(39,67)(40,47)(41,63)(42,69)(44,72)(45,74)(46,75)(51,78)(52,80)(53,84)(54,81)(55,82)(57,73)(58,85)(60,86)(61,87)(64,88)(65,89)(66,79)(68,77)(70,90)(71,76)(83,91)

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, 5156);