C₁₁×#13420 #14590613

order	2816
nilpotency class	4
isoclinism	isoclinic class of #13343
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#13420

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×D₄	C₂³×C₁₁
prime radical	C₂×C₁₁×#120	C₂²
LCS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₁₁ ◁ C₂²×D₄×C₁₁ ◁ G

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

normal subgroups only

This group has 600 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) = 31
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 3 generators on 31 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,14)(16,17,20,23)(18,24,26,31)(19,22,27,30)(21,28,29,25);(12,13)(14,15)(19,27)(22,30);(12,14,15,13)(16,18)(17,21)(19,25)(20,26)(22,24)(23,29)(27,28)(30,31)

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, 6408);