C₁₉×#13671 #18019630

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13669
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13671

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2184
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
prime radical	C₁₉×#3415	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#131 ◁ C₁₉×#504 ◁ 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)(20,21,27,34)(22,35,39,64)(23,40,46,73)(24,33,26,31)(25,49,51,65)(28,52,56,36)(29,47,58,37)(30,59,63,44)(32,48,67,42)(38,70,71,57)(41,66,76,83)(43,53,45,72)(50,60,80,82)(54,69,68,75)(55,79,81,74)(61,78,62,77);(20,22)(21,28)(23,41)(24,37)(25,50)(26,47)(27,39)(29,53)(30,60)(31,54)(32,66)(33,68)(34,56)(35,40)(36,44)(38,42)(43,74)(45,79)(46,76)(48,71)(49,55)(51,80)(52,59)(57,62)(58,72)(61,70)(63,82)(64,73)(65,81)(67,83)(69,78)(75,77);(20,22)(21,29)(23,36)(24,47)(25,38)(26,37)(27,39)(28,53)(30,55)(31,64)(32,57)(33,35)(34,58)(40,68)(41,44)(42,50)(43,75)(45,69)(46,52)(48,80)(49,60)(51,71)(54,73)(56,72)(59,76)(61,83)(62,66)(63,81)(65,82)(67,70)(74,77)(78,79)

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6659);