C₁₉×#10211 #18016170

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10208
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#10211

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#127
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

406 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 94 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)(20,21,28,34)(22,35,41,49)(23,42,46,37)(24,47,52,70)(25,53,58,66)(26,36,60,72)(27,33,56,69)(29,61,39,43)(30,63,67,51)(31,57,71,83)(32,50,73,76)(38,74,65,82)(40,64,75,81)(44,80,59,54)(45,78,79,48)(55,77,68,62);(20,22,27,40)(21,23,33,45)(24,48,51,37)(25,54,57,38)(26,29,50,62)(28,41,56,75)(30,64,47,35)(31,68,66,43)(32,59,72,82)(34,46,69,79)(36,74,73,44)(39,76,77,60)(42,52,78,63)(49,67,81,70)(53,61,71,55)(58,80,83,65);(20,23,27,45)(21,29,33,62)(22,36,40,73)(24,49,51,81)(25,55,57,61)(26,59,50,82)(28,46,56,79)(30,65,47,80)(31,48,66,37)(32,41,72,75)(34,39,69,77)(35,63,64,52)(38,70,54,67)(42,71,78,53)(43,58,68,83)(44,76,74,60)

Conjugacy classes & character table

475 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 3199);