C₁₁×#13666 #14590859

order	2816
nilpotency class	5
isoclinism	isoclinic class of #13661
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#13666

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₁
prime radical	C₂×C₁₁×#508	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂²×C₈×C₁₁ ◁ C₂²×C₁₁×C₁₆ ◁ G

288 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 79
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 3 generators on 79 points:

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

Conjugacy classes & character table

539 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 6654);