C₁₉×#13690 #18019649

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13661
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#13690

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
prime radical	C₂×C₁₉×D₁₆	C₂²
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

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

normal subgroups only

This group has 204 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) = 87
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 87 points:

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

Conjugacy classes & character table

931 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6678);