C₁₁×#11484 #14588677

order	2816
nilpotency class	4
isoclinism	isoclinic class of #2121
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#11484

Subgroups

	subgroup	G/H
center	C₄×C₁₁	C₂×#99
commutator	C₂³	C₂²×C₈×C₁₁
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₁
socle	C₂×C₁₁	#1459
prime radical	C₁₁×#525	C₄
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂×C₈×C₁₁ ◁ C₂×C₁₁×#131 ◁ G

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

normal subgroups only

This group has 368 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) = 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)(12,13,15,20,16,21,26,33,17,18,25,29,27,30,37,40)(14,19,23,31,24,32,36,41,22,28,34,38,35,39,42,43);(13,18)(14,22)(21,30)(23,34)(24,35)(31,38)(36,42)(41,43);(12,14,16,24,17,22,27,35)(13,19,21,32,18,28,30,39)(15,23,26,36,25,34,37,42)(20,31,33,41,29,38,40,43)

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, 4472);