C₁₉×#13669 #18019628

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

Aliases

direct product

C₁₉×#13669

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2184
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

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

normal subgroups only

This group has 288 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)(22,35)(23,40)(24,33)(25,49)(26,31)(27,34)(28,36)(29,37)(30,44)(32,42)(38,69)(39,62)(41,64)(43,52)(45,71)(46,72)(47,57)(48,65)(50,58)(51,63)(53,74)(54,73)(55,68)(56,70)(59,76)(60,77)(61,78)(66,67)(75,83)(79,81)(80,82);(20,22)(21,28)(23,41)(24,37)(25,50)(26,47)(27,39)(29,52)(30,58)(31,53)(32,64)(33,66)(34,55)(35,40)(36,44)(38,42)(43,73)(45,79)(46,75)(48,70)(49,54)(51,80)(56,60)(57,71)(59,69)(61,82)(62,72)(63,81)(65,83)(67,77)(68,78)(74,76);(20,22)(21,29)(23,36)(24,47)(25,38)(26,37)(27,39)(28,52)(30,54)(31,62)(32,56)(33,35)(34,57)(40,66)(41,44)(42,50)(43,74)(45,67)(46,68)(48,80)(49,58)(51,70)(53,72)(55,71)(59,83)(60,64)(61,81)(63,82)(65,69)(73,76)(75,78)(77,79)

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, 6657);