C₁₁×#13664 #14590857

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

Aliases

direct product

C₁₁×#13664

Subgroups

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

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

normal subgroups only

This group has 324 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) = 704

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)(16,17,21,26)(18,22,30,37)(19,31,33,47)(20,34,32,25)(23,38,40,27)(24,41,42,28)(29,43,44,36)(35,46,39,45);(17,22)(18,27)(19,28)(20,32)(23,24)(25,43)(26,37)(29,46)(30,38)(31,35)(33,41)(34,36)(39,47)(40,42)(44,45);(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, 6652);