C₁₁×#7192 #14584385

order	2816
nilpotency class	4
isoclinism	isoclinic class of AΣL(1,𝔽₁₆)
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#7192

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#99
commutator	C₂³	C₄×C₈×C₁₁
Frattini, cosocle	C₂²×M₁₆	C₂²×C₁₁
socle	C₂²×C₁₁	#324
prime radical	C₂⁴×C₁₁	C₂×C₈
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂²×C₁₁×M₁₆ ◁ G

310 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 704

A minimal faithful permutation representation — 2 generators on 47 points:

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

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 180);