C₁₁×#13572 #14590765

order	2816
nilpotency class	5
isoclinism	isoclinic class of #1404
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#13572

Subgroups

	subgroup	G/H
center	C₄×C₁₁	AΣL(1,𝔽₁₆)
commutator	C₂×Q₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₄⋊Q₈	C₂³×C₁₁
socle	C₂×C₁₁	C₂×AΣL(1,𝔽₁₆)
prime radical	C₁₁×#3018	C₂
LCS	G ▷ C₂×Q₈ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₁₁×#532 ◁ G

482 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 43
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 3 generators on 43 points:

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

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 6560);