C₁₁×#13459 #14590652

order	2816
nilpotency class	4
isoclinism	isoclinic class of #13459
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#13459

Subgroups

	subgroup	G/H
center	C₄×C₁₁	#498
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
socle	C₂×C₁₁	#2058
prime radical	C₂³×C₁₁	AGL(1,ℤ/8)
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×#97 ◁ G

318 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 118 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)(12,13)(14,23,25,40)(15,28)(16,21)(17,33)(18,22)(19,26,35,42)(20,32)(24,37,27,39)(29,43)(30,34,41,38)(31,36);(14,24,25,27)(15,29)(19,34,35,38)(20,36)(23,39,40,37)(26,30,42,41)(28,43)(31,32);(12,14,17,24,18,25,16,27)(13,19,21,38,22,35,33,34)(15,30,32,26,29,41,31,42)(20,37,28,23,36,39,43,40)

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, 6447);