C₁₁×#10083 #14587276

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10078
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#10083

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₁	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂²×D₄×C₁₁	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

526 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 47
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 3 generators on 47 points:

(1,2,3,4,5,6,7,8,9,10,11)(16,17,21,25)(18,26,28,31)(19,24,20,23)(22,29,30,27)(32,33,36,39)(34,40,42,47)(35,43,45,38)(37,44,46,41);(12,13)(14,15)(16,18)(17,22)(19,29)(20,27)(21,28)(23,31)(24,26)(25,30)(32,34,36,42)(33,37,39,46)(35,44,45,41)(38,47,43,40);(13,15)(16,18)(17,22)(19,27)(20,29)(21,28)(23,26)(24,31)(25,30)(35,45)(38,43)(40,47)(41,44)

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 3071);