C₁₉×#13708 #18019667

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

Aliases

direct product

C₁₉×#13708

Subgroups

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

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

normal subgroups only

This group has 158 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) = 4864

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

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, 6696);