C₁₁×#7068 #14584261

order	2816
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁×C₁₆ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#7068

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₁	D₈
commutator	C₈	C₂×C₁₁×C₁₆
Frattini, cosocle	C₈²	C₂²×C₁₁
socle	C₂²×C₁₁	D₄⋊C₈
prime radical	C₂×C₁₁×D₈	C₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₁ ◁ C₄×C₈×C₁₁ ◁ C₈²×C₁₁ ◁ G

162 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 43
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 2 generators on 43 points:

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

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, 56);