C₁₁×#10085 #14587278

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10078
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₁×#10085

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₁	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₁₁×#2819	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

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

normal subgroups only

This group has 600 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) = 39
transitive degree	μ_t(G) = 1408

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

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

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, 3073);