C₁₁×#13458 #14590651

order	2816
nilpotency class	4
isoclinism	isoclinic class of #13371
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#13458

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#476
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

324 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 122 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)(16,17,19,23)(18,28)(20,34,33,44)(21,27,22,26)(24,40)(25,36,39,37)(29,43)(30,38)(31,45)(32,46)(35,41)(42,47);(12,13)(14,15)(17,23)(18,29,32,31)(24,41,38,42)(25,39)(26,27)(28,43,46,45)(30,47,40,35)(34,44);(13,15)(16,18,21,31,19,32,22,29)(17,24,26,41,23,38,27,42)(20,35,36,40,33,47,37,30)(25,43,44,46,39,45,34,28)

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, 6446);