C₁₁×#7812 #14585005

order	2816
nilpotency class	3
isoclinism	isoclinic class of #7734
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₁×#7812

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
LCS	G ▷ C₂×C₄² ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

398 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 2816

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,16)(14,18)(17,19)(21,24)(22,26)(25,27)(28,29,32,35)(30,33,37,40)(31,34,38,41)(36,42,43,39);(12,13,15,17)(14,19,18,16)(28,30)(29,33)(31,36)(32,37)(34,39)(35,40)(38,43)(41,42);(20,21,23,25)(22,27,26,24)(28,31)(29,34)(30,36)(32,38)(33,39)(35,41)(37,43)(40,42)

Conjugacy classes & character table

407 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 800);