C₁₁×#13421 #14590614

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

Aliases

direct product

C₁₁×#13421

Subgroups

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

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

normal subgroups only

This group has 496 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) = 704

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

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

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, 6409);