C₁₉×#13702 #18019661

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13700
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#13702

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2215
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
prime radical	C₁₉×#2221	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#131 ◁ C₁₉×#504 ◁ G

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

normal subgroups only

This group has 184 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)(21,28)(22,35)(23,39)(24,26)(25,40)(29,43)(30,57)(31,51)(32,63)(33,49)(34,52)(36,67)(37,70)(38,44)(41,55)(42,56)(45,46)(47,58)(48,50)(53,62)(54,71)(59,78)(60,76)(61,75)(64,77)(65,68)(69,79)(73,81)(74,80)(82,83);(20,21,29,53,25,32,42,51,24,31,55,63,45,62,23,28,27,34,39,50,46,64,41,49,26,33,56,77,40,48,43,52)(22,30,54,78,37,59,65,57,44,61,67,81,72,82,36,47,38,60,68,74,70,80,71,76,35,58,79,83,66,73,69,75);(20,22)(21,30)(23,36)(24,44)(25,37)(26,35)(27,38)(28,47)(29,54)(31,61)(32,59)(33,58)(34,60)(39,68)(40,66)(41,71)(42,65)(43,69)(45,72)(46,70)(48,73)(49,76)(50,74)(51,57)(52,75)(53,78)(55,67)(56,79)(62,82)(63,81)(64,80)(77,83)

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, 6690);