C₁₁×#7160 #14584353

order	2816
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#7160

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₁	D₈
commutator	C₈	C₄×C₈×C₁₁
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₁
socle	C₂²×C₁₁	#335
prime radical	C₂³×C₁₁	#108
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₁ ◁ C₂²×C₈×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

210 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 126 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)(16,17,19,26,22,27,35,41,23,28,36,42,21,37,20,25)(18,29,30,24,33,38,45,39,34,44,46,40,32,47,31,43);(13,15)(16,18,20,31,21,32,36,46,23,34,35,45,22,33,19,30)(17,24,26,38,27,39,41,44,28,40,42,47,37,43,25,29)

Conjugacy classes & character table

968 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 148);