C₁₁×#13457 #14590650

order	2816
nilpotency class	4
isoclinism	isoclinic class of #13371
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#13457

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#476
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₂³×C₁₁	AGL(1,ℤ/8)
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

356 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 122 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)(17,22,24,31)(18,26)(19,20)(23,27,25,30)(28,29);(12,13)(14,15)(17,23,24,25)(22,30,31,27);(13,15)(16,17,20,23,21,24,19,25)(18,27,26,22,29,30,28,31)

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 6445);