C₁₁×#9016 #14586209

order	2816
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#9016

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₁	#120
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₂⁵×C₁₁	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

836 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 150 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) = 39
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 39 points:

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

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, 2004);