C₁₁×#10119 #14587312

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10104
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#10119

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂³×C₁₁	#121
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

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

normal subgroups only

This group has 454 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) = 1408

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

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

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, 3107);