C₁₉×#13730 #18019689

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13697
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#13730

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

232 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 86 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)(24,25,30,35)(26,36,38,59)(27,42,45,74)(28,46,48,76)(29,49,47,34)(31,50,51,39)(32,54,56,37)(33,57,58,43)(40,70,66,87)(41,71,67,62)(44,75,64,73)(52,82,81,86)(53,69,77,80)(55,65,72,83)(60,79,84,63)(61,78,85,68);(24,26,37,63,28,40,64,80,47,67,83,82,57,78,45,50,30,38,54,79,48,66,44,69,29,41,65,86,43,68,27,39)(25,31,42,61,33,52,72,71,49,77,75,87,76,84,56,59,35,51,74,85,58,81,55,62,34,53,73,70,46,60,32,36);(20,21,22,23)(26,38)(31,51)(36,59)(39,50)(40,66)(41,67)(52,81)(53,77)(60,84)(61,85)(62,71)(63,79)(68,78)(69,80)(70,87)(82,86)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6718);