C₁₁×#13415 #14590608

order	2816
nilpotency class	4
isoclinism	isoclinic class of #13331
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#13415

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#459
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₂³×C₁₁	AGL(1,ℤ/8)
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

436 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 114 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)(16,17,23,29)(18,21,32,39)(19,30,36,46)(20,28,22,26)(24,27,37,31)(25,41,43,35)(33,38,42,47)(34,44,40,45);(16,18,23,32)(17,24,29,37)(19,33,36,42)(20,27,22,31)(21,26,39,28)(25,34,43,40)(30,41,46,35)(38,45,47,44);(13,15)(16,19,20,34,23,36,22,40)(17,25,26,42,29,43,28,33)(18,30,31,45,32,46,27,44)(21,38,37,35,39,47,24,41)

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, 6403);