C₁₃×#13665 #15700004

order	3328
nilpotency class	5
isoclinism	isoclinic class of #13661
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13665

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
prime radical	C₂³×C₁₃	D₁₆
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂²×C₈×C₁₃ ◁ C₂²×C₁₃×C₁₆ ◁ G

284 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 81
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 3 generators on 81 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,24,29)(20,30,34,61)(21,35,40,59)(22,41,44,75)(23,45,43,28)(25,47,50,31)(26,51,54,38)(27,55,57,37)(32,63,64,80)(33,65,46,60)(36,56,70,81)(39,73,72,67)(42,52,76,79)(48,74,77,69)(49,62,58,68)(53,71,66,78);(18,20,24,34)(19,25,29,50)(21,36,40,70)(22,42,44,76)(23,46,43,33)(26,52,54,79)(27,56,57,81)(28,58,45,49)(30,59,61,35)(31,51,47,38)(32,55,64,37)(39,74,72,69)(41,48,75,77)(53,80,66,63)(60,67,65,73)(62,71,68,78);(15,17)

Conjugacy classes & character table

637 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6653);