C₁₁×#13373 #14590566

order	2816
nilpotency class	4
isoclinism	isoclinic class of #13373
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#13373

Subgroups

	subgroup	G/H
center	C₄×C₁₁	#486
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
socle	C₂×C₁₁	#2023
prime radical	C₂×C₁₁×#135	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×#97 ◁ G

364 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 110 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)(24,41,27,37)(29,39)(30,38,43,34)(31,36);(14,24,25,27)(15,29)(19,34,35,38)(20,36)(23,37,40,41)(26,43,42,30)(28,39)(31,32);(12,14)(13,19)(15,30)(16,27)(17,24)(18,25)(20,37)(21,38)(22,35)(23,39)(26,31)(28,40)(29,43)(32,42)(33,34)(36,41)

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, 6361);