C₁₁×#12046 #14589239

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

Aliases

direct product

C₁₁×#12046

Subgroups

	subgroup	G/H
center	C₁₁×C₁₆	D₈
commutator	C₈	C₂²×C₈×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
socle	C₂×C₁₁	C₈×D₈
prime radical	C₁₁×#508	C₄
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₁×C₁₆ ◁ C₂×C₁₁×C₁₆ ◁ C₄×C₁₁×C₁₆ ◁ G

216 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 352

A minimal faithful permutation representation — 3 generators on 43 points:

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

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, 5034);