C₁₉×#13718 #18019677

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13717
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#13718

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2233
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
prime radical	C₂³×C₁₉	SD₃₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ C₂×C₁₉×M₃₂ ◁ G

160 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 66 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)(22,32,33,61)(23,37,38,71)(24,43,46,79)(25,47,45,30)(27,49,50,34)(28,53,54,41)(29,57,59,40)(35,69,65,83)(36,70,48,64)(39,75,67,58)(42,62,74,73)(44,63,80,55)(51,76,82,78)(52,68,60,81)(56,77,72,66);(23,38)(28,54)(32,61)(34,49)(37,71)(39,67)(41,53)(42,74)(55,63)(56,72)(62,73)(64,70)(66,77)(68,81)(69,83)(76,78);(20,22,25,48,26,33,45,36)(21,27,30,60,31,50,47,52)(23,39,42,78,38,67,74,76)(24,44,40,35,46,80,57,65)(28,55,56,69,54,63,72,83)(29,58,43,51,59,75,79,82)(32,62,70,37,61,73,64,71)(34,66,81,41,49,77,68,53)

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, 6706);