C₁₁×#9028 #14586221

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

Aliases

direct product

C₁₁×#9028

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

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

normal subgroups only

This group has 696 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)(16,17,21,22,20,18,19,23)(24,25)(26,29)(27,34,35,30)(28,31)(32,36,38,39)(33,37);(12,13,14,15)(16,18,20,17)(19,23,21,22)(24,26,28,33)(25,29,31,37)(27,32,35,38)(30,36,34,39);(16,19,20,21)(17,22,18,23)(24,27,28,35)(25,30,31,34)(26,32,33,38)(29,36,37,39)

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, 2016);