C₁₉×#13668 #18019627

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13667
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13668

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2184
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
prime radical	C₁₉×#3414	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ C₂×C₁₉×M₃₂ ◁ G

284 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 74 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)(20,21,26,31)(22,32,34,61)(23,37,39,67)(24,43,46,77)(25,47,45,30)(27,49,50,33)(28,53,55,41)(29,57,59,40)(35,65,64,82)(36,66,48,62)(38,58,70,83)(42,75,73,69)(44,54,78,81)(51,76,79,72)(52,63,60,71)(56,74,68,80);(20,22)(21,27)(23,38)(24,44)(25,48)(26,34)(28,54)(29,58)(30,60)(31,50)(32,37)(33,41)(35,40)(36,45)(39,70)(42,76)(43,51)(46,78)(47,52)(49,53)(55,81)(56,82)(57,64)(59,83)(61,67)(62,75)(63,80)(65,68)(66,69)(71,74)(72,73)(77,79);(23,39)(28,55)(32,61)(33,49)(37,67)(38,70)(41,53)(42,73)(54,81)(56,68)(62,66)(63,71)(65,82)(69,75)(72,76)(74,80)

Conjugacy classes & character table

589 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6656);