C₁₁×#11456 #14588649

order	2816
nilpotency class	4
isoclinism	isoclinic class of #2127
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#11456

Subgroups

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

364 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 138 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)(12,13,16,21,17,20,31,36,18,22,32,38,15,28,29,37)(14,23,26,40,27,34,41,43,24,39,30,42,25,19,33,35);(12,14)(13,19,22,34)(15,25)(16,30)(17,27)(18,24)(20,23,28,39)(21,35,38,43)(26,32)(29,41)(31,33)(36,40,37,42);(14,24)(19,34)(23,39)(25,27)(26,30)(33,41)(35,43)(40,42)

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4444);