C₁₁×#7155 #14584348

order	2816
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁×#7155

Subgroups

	subgroup	G/H
center	C₄²×C₁₁	D₈
commutator	C₈	C₄×C₈×C₁₁
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₁
socle	C₂²×C₁₁	#340
prime radical	C₂³×C₁₁	#106
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

222 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 134 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) = 1408

A minimal faithful permutation representation — 2 generators on 51 points:

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

Conjugacy classes & character table

968 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 143);