C₁₁×#8915 #14586108

order	2816
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#8915

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	#120
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

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

normal subgroups only

This group has 396 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) = 47
transitive degree	μ_t(G) = 2816

A minimal faithful permutation representation — 3 generators on 47 points:

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

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, 1903);