C₁₉×#13688 #18019647

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

Aliases

direct product

C₁₉×#13688

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

200 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 4864

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

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, 6676);