C₁₁×#9512 #14586705

order	2816
nilpotency class	3
isoclinism	isoclinic class of #9495
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₁×#9512

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#386
commutator	C₂⁴	C₂²×C₄×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₂⁵×C₁₁	C₂×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

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

normal subgroups only

This group has 558 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)(12,13,17,22,16,14,19,25)(15,20,27,36,26,23,31,38)(18,21,32,33,29,24,34,30)(28,37,41,42,39,35,43,40);(12,14,17,30,16,13,19,33)(15,23,31,42,26,20,27,40)(18,24,32,25,29,21,34,22)(28,35,43,36,39,37,41,38);(12,15,18,28)(13,20,21,37)(14,23,24,35)(16,26,29,39)(17,31,32,43)(19,27,34,41)(22,38,33,40)(25,36,30,42)

Conjugacy classes & character table

407 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 2500);