C₁₁×#12066 #14589259

order	2816
nilpotency class	4
isoclinism	isoclinic class of #2180
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12066

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₁	#442
commutator	C₈	C₂²×C₈×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₁₁×#322 ◁ G

214 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 51
transitive degree	μ_t(G) = 2816

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,18,16,14,17,19)(20,21,24,30,26,31,25,28)(22,32,34,49,36,50,35,46)(23,37,40,47,39,45,41,29)(27,42,43,33,44,38,48,51);(20,22,26,36)(21,27,31,44)(23,38,39,42)(24,35,25,34)(28,43,30,48)(29,46,47,49)(32,37,50,45)(33,41,51,40);(12,14,15,19,16,13,17,18)(21,28,31,30)(23,39)(27,43,44,48)(29,37,47,45)(32,46,50,49)(33,51)(38,42)(40,41)

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5054);