C₁₁×#7115 #14584308

order	2816
nilpotency class	4
isoclinism	isoclinic class of #1355
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁×#7115

Subgroups

	subgroup	G/H
center	C₄×C₁₁	#329
commutator	C₄²	C₂×C₈×C₁₁
Frattini, cosocle	#376	C₂²×C₁₁
socle	C₂×C₁₁	#1270
prime radical	C₁₁×#532	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₁₁×#376 ◁ G

248 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 70 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 — 2 generators on 43 points:

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

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 103);