C₁₉×#13700 #18019659

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

Aliases

direct product

C₁₉×#13700

Subgroups

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

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

normal subgroups only

This group has 188 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)(23,29)(24,26)(25,39)(30,56)(31,50)(32,62)(33,48)(34,51)(36,66)(37,68)(38,43)(40,54)(41,53)(42,55)(44,45)(46,57)(47,49)(52,64)(58,81)(59,74)(60,73)(61,76)(63,75)(67,78)(69,77)(71,80)(72,79)(82,83);(20,21,29,49,25,32,40,48,24,31,53,75,44,61,42,51,27,34,55,76,45,63,41,50,26,33,54,62,39,47,23,28)(22,30,52,72,37,58,69,74,43,60,78,83,70,82,67,73,38,59,77,81,68,79,64,56,35,57,66,80,65,71,36,46);(20,22)(21,30)(23,36)(24,43)(25,37)(26,35)(27,38)(28,46)(29,52)(31,60)(32,58)(33,57)(34,59)(39,65)(40,69)(41,64)(42,67)(44,70)(45,68)(47,71)(48,74)(49,72)(50,56)(51,73)(53,78)(54,66)(55,77)(61,82)(62,80)(63,79)(75,83)(76,81)

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, 6688);