C₁₁×#10387 #14587580

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10386
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#10387

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#393
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₂⁴×C₁₁	C₂×D₄
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

414 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 352

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

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

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, 3375);