C₁₁×#12112 #14589305

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12108
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#12112

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₂×C₁₁×#41	D₄
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₁₁×#408 ◁ G

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

normal subgroups only

This group has 390 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) = 1408

A minimal faithful permutation representation — 3 generators on 83 points:

(1,2,3,4,5,6,7,8,9,10,11)(16,19)(20,21,27,33)(22,34,38,62)(23,39,42,59)(24,43,47,57)(25,32,26,31)(28,50,53,36)(29,48,55,41)(30,45,58,46)(35,63,67,80)(37,68,49,56)(40,71,74,54)(44,60,75,52)(51,72,79,83)(61,66,82,65)(64,69,77,78)(70,76,81,73);(12,13)(14,16)(15,17)(18,19)(20,22,27,38)(21,28,33,53)(23,35,42,67)(24,44,47,75)(25,37,26,49)(29,51,55,79)(30,56,58,68)(31,52,32,60)(34,57,62,43)(36,45,50,46)(39,69,59,78)(40,72,74,83)(41,65,48,66)(54,80,71,63)(61,81,82,70)(64,76,77,73);(12,14)(13,16)(15,18)(17,19)(20,23)(21,29)(22,35)(24,40)(25,48)(26,41)(27,42)(28,51)(30,54)(31,59)(32,39)(33,55)(34,61)(36,64)(37,66)(38,67)(43,70)(44,72)(45,76)(46,73)(47,74)(49,65)(50,77)(52,78)(53,79)(56,80)(57,81)(58,71)(60,69)(62,82)(63,68)(75,83)

Conjugacy classes & character table

341 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5100);