C₁₁×#10383 #14587576

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10382
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#10383

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

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

normal subgroups only

This group has 404 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)(13,18,20,31)(14,22)(15,27)(19,35,36,30)(21,34,32,23)(25,41)(26,39)(28,29)(33,37,40,43)(38,42);(13,19,20,36)(14,22)(15,28)(18,30,31,35)(21,37,32,43)(23,40,34,33)(25,42)(26,39)(27,29)(38,41);(12,13,17,21)(14,23,22,31)(15,19,29,37)(16,20,24,32)(18,26,34,39)(25,35,38,40)(27,43,28,36)(30,42,33,41)

Conjugacy classes & character table

341 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 3371);