C₁₁×#7466 #14584659

order	2816
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₁×C₁₆ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#7466

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₁	C₄²
commutator	C₄	C₄×C₁₁×C₁₆
Frattini, cosocle	C₂²×C₁₆	C₂²×C₁₁
socle	C₂²×C₁₁	#346
prime radical	C₂³×C₁₁	M₃₂
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₁ ◁ G

182 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 118 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 — 2 generators on 47 points:

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

Conjugacy classes & character table

968 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 454);