C₁₉×#13666 #18019625

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

Aliases

direct product

C₁₉×#13666

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
prime radical	C₂×C₁₉×#508	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ C₂²×C₁₆×C₁₉ ◁ G

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

normal subgroups only

This group has 288 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)(24,25,30,36)(26,37,42,68)(27,32,45,35)(28,46,49,80)(29,50,52,58)(31,53,56,39)(33,59,62,48)(34,63,65,44)(38,67,41,74)(40,72,73,86)(43,75,78,79)(47,64,82,87)(51,60,70,85)(54,71,66,69)(55,76,83,81)(57,84,61,77);(24,26)(25,31)(27,38)(28,47)(29,51)(30,42)(32,54)(33,60)(34,64)(35,66)(36,56)(37,46)(39,48)(40,44)(41,45)(43,76)(49,82)(50,55)(52,70)(53,59)(57,72)(58,83)(61,86)(62,85)(63,73)(65,87)(67,75)(68,80)(69,77)(71,84)(74,79)(78,81);(21,23)(24,27,30,45)(25,32,36,35)(26,38,42,41)(28,43,49,78)(29,44,52,63)(31,54,56,66)(33,57,62,61)(34,58,65,50)(37,67,68,74)(39,69,53,71)(40,70,73,51)(46,75,80,79)(47,76,82,81)(48,77,59,84)(55,64,83,87)(60,72,85,86)

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, 6654);