C₁₁×#13663 #14590856

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

Aliases

direct product

C₁₁×#13663

Subgroups

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

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

normal subgroups only

This group has 298 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) = 47
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 3 generators on 47 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(17,23)(18,22)(19,29)(21,31)(24,39)(25,38)(26,41)(27,42)(28,34)(30,35)(32,44)(33,43)(36,37)(40,46)(45,47);(16,17)(18,24)(19,30)(20,25)(21,35)(22,36)(23,29)(26,31)(27,41)(28,40)(32,45)(33,46)(34,47)(37,43)(38,44)(39,42);(13,15)(16,18,20,22)(17,24,25,36)(19,27,32,33)(21,28,34,31)(23,37,38,39)(26,35,40,47)(29,43,44,42)(30,41,45,46)

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, 6651);