C₁₁×#7467 #14584660

order	2816
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₁×C₁₆ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#7467

Subgroups

	subgroup	G/H
center	C₂×C₁₁×C₁₆	D₄
commutator	C₄	C₄×C₁₁×C₁₆
Frattini, cosocle	C₂²×C₁₆	C₂²×C₁₁
socle	C₂²×C₁₁	C₄⋊C₁₆
prime radical	C₂³×C₁₁	M₃₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁×C₁₆ ◁ C₂²×C₁₁×C₁₆ ◁ G

190 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 118 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)(12,13)(14,15)(16,17,19,25,20,27,30,40,21,24,31,37,33,38,43,46,22,26,32,39,34,41,44,47,18,23,28,35,29,36,42,45);(13,15)(17,23,26,24)(25,35,39,37)(27,36,41,38)(40,45,47,46)

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 455);