C₁₁×#9981 #14587174

order	2816
nilpotency class	3
isoclinism	isoclinic class of #9980
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#9981

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₁₁×#3006	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

764 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 35
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

308 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 2969);