C₁₁×#11483 #14588676

order	2816
nilpotency class	4
isoclinism	isoclinic class of AΣL(1,𝔽₁₆)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#11483

Subgroups

	subgroup	G/H
center	C₈×C₁₁	#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 ◁ C₈×C₁₁ ◁ C₂×C₈×C₁₁ ◁ C₂×C₁₁×#131 ◁ G

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

normal subgroups only

This group has 382 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)(14,19,22,31,23,32,35,41,24,28,34,38,36,39,42,43);(13,18)(19,28)(21,30)(32,39);(12,14,16,23,17,24,27,36)(13,19,21,32,18,28,30,39)(15,22,26,35,25,34,37,42)(20,31,33,41,29,38,40,43)

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4471);