C₁₉×#13716 #18019675

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13661
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#13716

Subgroups

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

168 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 70 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)(20,21)(22,25)(23,24)(26,27)(28,29,34,40)(30,35,44,57)(31,36,48,60)(32,49,51,78)(33,52,50,39)(37,61,63,45)(38,64,65,46)(41,53,70,81)(42,71,73,91)(43,74,72,56)(47,66,75,59)(54,82,84,67)(55,85,86,68)(58,77,62,76)(69,87,88,80)(79,90,83,89);(21,24)(25,27)(28,30,34,44)(29,35,40,57)(31,41,48,70)(32,42,51,73)(33,43,50,72)(36,53,60,81)(37,54,63,84)(38,55,65,86)(39,56,52,74)(45,67,61,82)(46,68,64,85)(47,69,75,88)(49,71,78,91)(58,79,62,83)(59,80,66,87)(76,89,77,90);(20,22,23,26)(21,25,24,27)(29,36)(31,45)(32,46)(33,50)(35,53)(37,38)(39,66)(40,60)(41,67)(42,68)(43,72)(47,77)(48,61)(49,58)(51,64)(52,59)(54,55)(56,87)(57,81)(62,78)(63,65)(69,90)(70,82)(71,79)(73,85)(74,80)(75,76)(83,91)(84,86)(88,89)

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, 6704);