C₁₉×#13695 #18019654

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13694
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#13695

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

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

normal subgroups only

This group has 194 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) = 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)(20,21)(22,23)(24,25,30,35)(26,36,41,62)(27,42,45,74)(28,46,48,76)(29,49,47,34)(31,50,53,38)(32,54,56,37)(33,57,58,43)(39,68,70,87)(40,71,69,61)(44,75,64,73)(51,81,82,86)(52,67,77,80)(55,65,72,83)(59,79,84,63)(60,78,85,66);(24,26,37,63,28,39,64,80,47,69,83,81,57,78,45,50,30,41,54,79,48,70,44,67,29,40,65,86,43,66,27,38)(25,31,42,60,33,51,72,71,49,77,75,87,76,84,56,62,35,53,74,85,58,82,55,61,34,52,73,68,46,59,32,36);(21,23)

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6683);