C₁₁×#13662 #14590855

order	2816
nilpotency class	5
isoclinism	isoclinic class of #13661
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#13662

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₁
prime radical	C₁₁×#2215	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂²×C₈×C₁₁ ◁ C₂²×C₁₁×C₁₆ ◁ G

294 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 1408

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

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

Conjugacy classes & character table

539 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 6650);