C₁₉×#13693 #18019652

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13691
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#13693

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2206
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
prime radical	C₁₉×#508	C₂²
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

196 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 83
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 83 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,28,35)(22,33,39,54)(23,40,43,72)(24,34,27,31)(25,45,49,77)(26,29,38,55)(30,56,58,42)(32,60,63,47)(36,66,67,83)(37,59,69,62)(41,73,51,71)(44,53,48,76)(46,64,78,81)(50,61,70,82)(52,79,80,75)(57,74,65,68);(20,22,27,38,28,39,24,26)(21,29,34,54,35,55,31,33)(23,36,51,70,43,67,41,50)(25,37,48,60,49,69,44,47)(30,52,65,81,58,80,57,64)(32,53,62,77,63,76,59,45)(40,61,73,83,72,82,71,66)(42,46,68,79,56,78,74,75);(20,23)(21,30)(22,36)(24,41)(25,46)(26,50)(27,51)(28,43)(29,52)(31,57)(32,61)(33,64)(34,65)(35,58)(37,68)(38,70)(39,67)(40,45)(42,47)(44,75)(48,79)(49,78)(53,73)(54,81)(55,80)(56,60)(59,66)(62,83)(63,82)(69,74)(71,76)(72,77)

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6681);