C₁₁×#13416 #14590609

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

Aliases

direct product

C₁₁×#13416

Subgroups

	subgroup	G/H
center	C₄×C₁₁	#486
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
socle	C₂×C₁₁	#2041
prime radical	C₁₁×#3150	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×#97 ◁ G

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

normal subgroups only

This group has 442 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)(14,17)(15,28)(16,35)(18,27)(19,24)(20,26)(21,31)(22,37)(23,36)(25,34)(29,38)(30,43)(32,41)(33,42)(39,40);(12,14)(13,20)(15,29)(16,23)(17,35)(18,22)(19,27)(21,33)(24,36)(25,32)(26,37)(28,31)(30,41)(34,40)(38,43)(39,42);(12,15,16,30,19,34,37,33)(13,21,22,40,24,41,35,29)(14,25,26,43,27,28,23,42)(17,38,36,32,18,39,20,31)

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, 6404);